determine angle x ans y of picnic table with know 80 degree angle ### Example Problem for Educational Purposes: Determining Angles**Problem Statement:**Given that $ m \angle ABC = 80^\circ $, determine $ m \angle x $ and $ m \angle y $ so that the top of the table will be parallel to the ground.**Explanation:**In this problem, you are given an angle $ \angle ABC $ with a measure of $ 80^\circ $. To find the measures of angles $ x $ and $ y $, additional information or context about their relationships with angle $ ABC $ and each other is needed.- $ m \angle ABC $: the given angle with a measure of $ 80^\circ $.- $ \angle x $ and $ \angle y $: the angles we need to determine to ensure that a certain condition (the table being parallel to the ground) is met.To solve the problem, we typically need to know the geometric configuration involving these angles, such as whether they are part of a larger shape (e.g., triangle, rectangle) or if specific relationships (e.g., supplementary, complementary) are provided.When the problem involves making a surface parallel to the ground, we might consider concepts like corresponding angles (if there are parallel lines involved) and the properties of parallel lines intersected by a transversal.**Note:**Since the image only provides a partial view, and hence limited context, ensure to review the complete problem statement and diagrams (if any) provided in your textbook or resource material to solve the problem accurately. ### Angles on a Picnic Table#### Problem Statement:The legs of a picnic table form an isosceles triangle as indicated in the figure. The angle at the bottom of the isosceles triangle (∠BAC) measures 80°. The goal is to determine the measures of the other two angles x and y.#### Diagram Description:- There is a square picnic tabletop represented at the top of the diagram.- Below the tabletop, there are two legs represented as intersecting lines that form an "X" shape.- The intersection of the legs below the tabletop forms an isosceles triangle with vertices labeled A, B, and C, where ∠BAC = 80°.- The angles at the top of the legs where they meet the tabletop are labeled as x and y respectively.##### Analysis:Given that the triangle is isosceles and the angle between the two equal legs (at A) is 80°, you can find the measures of the other angles as follows:Since the sum of angles in any triangle is 180°:\[ ∠BAC + ∠BCA + ∠B = 180° \]\[ 80° + x + x = 180° \]\[ 80° + 2x = 180° \]\[ 2x = 100° \]\[ x = 50° \]So, the angles x and y (∠B and ∠C) are both 50° each.Thus, the angles of the isosceles triangle formed by the picnic table legs are:- ∠BAC = 80°- ∠B = 50° - ∠C = 50°This decomposition helps in practical applications such as design and load analysis in construction and engineering fields.

Answered: Image /qna-images/answer/09d19c93-43ae-4fed-8fe4-012576e34ffb.jpg

Answered: 70. Angles on a Picnic Table The legs…

Math

Geometry

70. Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the figure. If 80° C

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section: Chapter Questions

Problem 75RE

See similar textbooks

Related questions

Q: Find the acute angle of intersection between two lines.

Q: Cancel Save Question Find the value of all the unknown angles 15 *+ 20 G

Q: Calculate the unknown angles.

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: e measure of angle marked with a 3. 7x + 33 10v

A: The solution is :

Q: 3. If cot --2 and 0<e , then cos e

A: Solution

Q: Classify the triangle. A. 759 30 75

A: In this question we have to classify the triangles and we are given with the angles out of which all…

Q: 2) 8 Lo 11 C hyp opp to

Q: find all the missing angles

Q: 4. 50° 1 2 42° 3 25° m mz mz

A: Sum of angles of triangle is 180°.

Q: 19. SQUA is a square with SQ = 6. Refer to this picture to find the following angles and segments.…

Q: Determine angle x and y thank you

Q: Explain the relationships and theorems used. D.

A: The quadrilateral ABDE will a rhombus as BD=AE is given and AB=AE (as both are radii of the circle).…

Q: 10. *7x + 7) 10x -38 [VALUE OF X] [MISSING ANGLE]

A: We will make use of the fact that two corresponding angles are of same measure. And given angles are…

Q: atcutate angte Bcm 9cm 10cm

A: Given triangle has three sides Let us say Side A =10cm Side B = 8cm…

Q: *11x + 8, 6x + 252 [VALUE OF X] [MISSING ANGLE] 32 5.

A: Here the two given lines are parallel lines, this lines are cut by another line called transversal…

Q: 27 12 38

A: Given a right angled triangle. The angle can be found out using the trigonometric relation, tan…

Q: Sketch in standard position on a grid below the angles 5pi/3(as a solid line) and -2pi/3(as a dashed…

Q: A person stands 15 feet from the base of a telephone pole. He measures an angle of elevation of 52…

Q: 11x + 8 6x + 2 [VALUE OF X] [MISSING ANGLE] 5.

Q: what is the 2 missing angle

A: As shown in diagram, Let ABCD is quadrilateral.

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

determine angle x ans y of picnic table with know 80 degree angle

### Example Problem for Educational Purposes: Determining Angles

**Problem Statement:**

Given that $ m \angle ABC = 80^\circ $, determine $ m \angle x $ and $ m \angle y $ so that the top of the table will be parallel to the ground.

**Explanation:**

In this problem, you are given an angle $ \angle ABC $ with a measure of $ 80^\circ $. To find the measures of angles $ x $ and $ y $, additional information or context about their relationships with angle $ ABC $ and each other is needed.

- $ m \angle ABC $: the given angle with a measure of $ 80^\circ $.
- $ \angle x $ and $ \angle y $: the angles we need to determine to ensure that a certain condition (the table being parallel to the ground) is met.

To solve the problem, we typically need to know the geometric configuration involving these angles, such as whether they are part of a larger shape (e.g., triangle, rectangle) or if specific relationships (e.g., supplementary, complementary) are provided.

When the problem involves making a surface parallel to the ground, we might consider concepts like corresponding angles (if there are parallel lines involved) and the properties of parallel lines intersected by a transversal.

**Note:**
Since the image only provides a partial view, and hence limited context, ensure to review the complete problem statement and diagrams (if any) provided in your textbook or resource material to solve the problem accurately.

### Angles on a Picnic Table

#### Problem Statement:
The legs of a picnic table form an isosceles triangle as indicated in the figure. The angle at the bottom of the isosceles triangle (∠BAC) measures 80°. The goal is to determine the measures of the other two angles x and y.

#### Diagram Description:
- There is a square picnic tabletop represented at the top of the diagram.
- Below the tabletop, there are two legs represented as intersecting lines that form an "X" shape.
- The intersection of the legs below the tabletop forms an isosceles triangle with vertices labeled A, B, and C, where ∠BAC = 80°.
- The angles at the top of the legs where they meet the tabletop are labeled as x and y respectively.

##### Analysis:
Given that the triangle is isosceles and the angle between the two equal legs (at A) is 80°, you can find the measures of the other angles as follows:

Since the sum of angles in any triangle is 180°:
\[ ∠BAC + ∠BCA + ∠B = 180° \]
\[ 80° + x + x = 180° \]
\[ 80° + 2x = 180° \]
\[ 2x = 100° \]
\[ x = 50° \]

So, the angles x and y (∠B and ∠C) are both 50° each.

Thus, the angles of the isosceles triangle formed by the picnic table legs are:
- ∠BAC = 80°
- ∠B = 50°
- ∠C = 50°

This decomposition helps in practical applications such as design and load analysis in construction and engineering fields.

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ratios$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

To determine the angle of elevation of a star in the sky, you align the star and the top of the backboard of a basketball hoop that is 5 feet higher than your eyes in your line of vision (see figure). Your horizontal distance from the backboard is 12 feet. What is the angle of elevation of the star?
Measurement A city engineer plans to build a footbridge across a lake from point X to point Y, as shown in the picture below. To find the length of the footbridge, she draws a right triangle XYZ, with right angle at X. She measures the distance from X to Z, 800 feet, and from Y to Z, 1,000 feet. How long will the bridge be?
For the triangle shown, A=30, B=45, and a=32 centimeters. Find the remaining angle and sides.
Empire State Building You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82. The total height of the building is another 123 meters above the 86th floor. What is the approximate height of the building? One of your friends is on the 86th floor. What is the distance between you and your friend?
Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The window in Alberts room is 4.0 feet high and 6.5 feet wide. (Sec Figure 24.) a. Calculate the area of the floor surface in Alberts room that is illuminated by the sun when the angle of elevation of the sun is 84. b. One winter day the angle of elevation of the sun outside Alberts window is 37. Will the illuminated area of the floor in Alberts room be greater on the summer day, or on the winter day? Figure 24
If the angle of elevation to the sun is 74.3 when a flagpole casts a shadow of 22.5 feet, what is the height of the flagpole? a. 63.2 feet b. 79.5 feet c. 83.1 feet d. 80.0 feet