Need help ### Geometry Problem: Parallelogram Angle Calculation#### Given parallelogram PQRST, what is the measure of ∠Q?Below is a diagram of parallelogram PQRST, with angle measures represented as algebraic expressions:``` P S /-----\ / \Q --- --- R```#### Diagram Details:- P is the upper left vertex.- Q is the lower left vertex.- R is the lower right vertex.- S is the upper right vertex.- Angle ∠P is labeled as \(8x + 3\).- Angle ∠S is labeled as \(2x + 7\).#### Multiple Choice Options:- A) 41°- B) 17°- C) 71°- D) 139°#### Explanation:To solve for the measure of ∠Q, recall that opposite angles of a parallelogram are equal, and adjacent angles are supplementary (sum up to 180 degrees).Given:\[ \angle P + \angle Q = 180^\circ \]\[ \angle P = 8x + 3 \]\[ \angle S = 2x + 7 \]Since ∠P and ∠Q are adjacent angles:\[ (8x + 3) + (2x + 7) = 180^\circ \]\[ 10x + 10 = 180^\circ \]\[ 10x = 170^\circ \]\[ x = 17^\circ \]Substituting x back to find specific angle measures:\[ \angle P = 8(17) + 3 = 136 + 3 = 139^\circ \]\[ \angle Q = 180^\circ - 139^\circ = 41^\circ \]Therefore, the correct answer is:- **A) 41°**This problem is a good example of applying algebra to solve geometric properties of parallelograms.

Solving the problem by finding the required value.

Answered: Given parallelogram PQRS, what is the…

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Given parallelogram PQRS, what is the measure of LQ? P S 8x+3 2x+7 R OA 41° OB 17⁰ OC 71° OD 139⁰

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter3: Triangles

Section3.4: Basic Constructions Justified

Problem 37E: Draw an obtuse triangle and construct the three perpendicular bisectors of its sides. Do the...

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Need help

### Geometry Problem: Parallelogram Angle Calculation

#### Given parallelogram PQRST, what is the measure of ∠Q?

Below is a diagram of parallelogram PQRST, with angle measures represented as algebraic expressions:

```
P S
/-----\
/ \
Q --- --- R
```

#### Diagram Details:
- P is the upper left vertex.
- Q is the lower left vertex.
- R is the lower right vertex.
- S is the upper right vertex.
- Angle ∠P is labeled as \(8x + 3\).
- Angle ∠S is labeled as \(2x + 7\).

#### Multiple Choice Options:
- A) 41°
- B) 17°
- C) 71°
- D) 139°

#### Explanation:
To solve for the measure of ∠Q, recall that opposite angles of a parallelogram are equal, and adjacent angles are supplementary (sum up to 180 degrees).

Given:
\[ \angle P + \angle Q = 180^\circ \]
\[ \angle P = 8x + 3 \]
\[ \angle S = 2x + 7 \]

Since ∠P and ∠Q are adjacent angles:
\[ (8x + 3) + (2x + 7) = 180^\circ \]
\[ 10x + 10 = 180^\circ \]
\[ 10x = 170^\circ \]
\[ x = 17^\circ \]

Substituting x back to find specific angle measures:
\[ \angle P = 8(17) + 3 = 136 + 3 = 139^\circ \]
\[ \angle Q = 180^\circ - 139^\circ = 41^\circ \]

Therefore, the correct answer is:

- **A) 41°**

This problem is a good example of applying algebra to solve geometric properties of parallelograms.

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