The diagram below shows rectangle RSTU with two diagonals drawn. (6x-15)° 63° U To find the value of x, Justin wrote the following steps. 1. m/STR+ m/RTU = 90 2. m/RTU = 27° 3.6z-15 27 %3D 4. 6z = 42 5. z = 7 Which statement can be used to justify the first step? O The alternate interior angles formed by the diagonals are congruent. O The angles at each vertex of the rectangle are right angles. O Opposite angles in a rectangle are congruent. O The diagonals of a rectangle are congruent.

Q: If MZBCD= (4x – BAD = (105 + 3x)°,find the measure of arc 50) and measure of arc BAD. B arc BAD =

A: By using circle property, We calculate the value of arc BAD.

Q: 1. Evaluate: -5x°+ (64) 3 + 16

A:

Q: Find the value of x. 20 (3х-11)° OF 10 O G. 3 О Н. 9 O J. 17

A:

Q: Find the missing variables. 8. 115° (Зу- 10)° (5х + 20)4 A,

A:

Q: The diagram below shows rectangle RSTU with two diagonals drawn. (6x-15)° 63° T What is the measure…

A: Given geometry is rectangle with angle ∠T=63°.

Q: 16. On the graph, AC=AB, calculate "x": 20° 50° X 4x 80° AND

A: We have to find the value of x.

Q: 6. 60° y

A: This is, solved using sine and cosine formulas

Q: (7x- 12) 52 D (9x- 20)°

A:

Q: 3 Find the value of each variable. y 60° 32

A: This can be solved using trigonometry ratios

Q: 14. In the diagram at the right, identify all supplementary and complementary angles. Explain. Then…

A: Recall; Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees.

Q: 6x° dx Select one: A.1 В. 1 +C C. 1 46+366 *C D. 65 +C

A:

Q: mLC=110°, find mzD=? mLE=? m<F=? mLD=(x + 40 )° , m2C= (3x-20)°, find x mzD=?

A:

Q: The angle between y = 4x + 2 and y = -x+3 is: %3D 65° 75° O 47° O 59°

A: We will first find the slopes of the two given lines and then find the angle between them.

Q: 22. If z = -2 – 2i, then zº = а. 29 b. -(2°)i 6. -(21") d. -(212)i

A:

Q: e/measure of the missing variable or indicated angle/segment. (assume not to scale) 8. Find y. (5y)°…

A:

Q: What is the value of angle PRS? S P- 23° (9x + 2) R (5x − 1)°

A: This question can be solved using the concept of exterior angle theorem of a triangle.

Q: Your Turn: 4. What is the value of z? 95° 200

A: Topic- circle and tangent

Q: Find the values of x and y that make the red lines parallel and the blue lines parallel

A: we have to find angle x and y  from the following figure.

Q: (4x+5)° 3x

A: By this property Sum of adjacent angle in parallelogram is 180°.

Q: 13. 0 (4r-22) m/P = %3D (10r-4 R (r+11) mZR =

A:

Q: A lighthouse keeper 100 feet above water sees a boat sailing in a straight line directly toward er.…

A: It is given that a light house keeper 100 feet above the water.  ⇒heigth of the light house h=100…

Q: 1. Evaluate: -5x° + (64) 16

A:

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.