### Determining Missing Angles in a ParallelogramIn the image, we have the parallelogram RSTU with one angle measurement provided. The angle at vertex $ S $ is given as $ 70^\circ $.#### Question:**What are the missing angle measures in parallelogram RSTU?**#### Answer Choices:1. $ m \angle R = 70^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 110^\circ $2. $ m \angle R = 110^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 70^\circ $3. $ m \angle R = 110^\circ $, $ m \angle T = 70^\circ $, $ m \angle U = 110^\circ $4. $ m \angle R = 70^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 70^\circ $#### Diagram Explanation:The parallelogram RSTU is depicted with:- $ S $ positioned at the bottom left,- $ R $ at the bottom right,- $ T $ at the top right, and- $ U $ at the top left.The image indicates angle measurement at:- $ m \angle S = 70^\circ $.#### Analyzing Angles in Parallelograms:In a parallelogram:1. Opposite angles are equal.2. Consecutive angles are supplementary, meaning they add up to $ 180^\circ $.Given $ m \angle S = 70^\circ $:- $ m \angle R $, opposite to $ m \angle S $, also equals $ 70^\circ $.- Consecutive angles $ m \angle T $ and $ m \angle U $: - $ m \angle T = 180^\circ - 70^\circ = 110^\circ $ - $ m \angle U = 110^\circ $Therefore, the correct angle measures are:- $ m \angle R = 70^\circ $,- $ m \angle T = 110^\circ $,- $ m \angle U = 110^\circ $.Thus, the correct answer

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01:28:25 What are the missing angle measures in parallelogram 70° RSTU? mzR = 70°, mLT = 110°, mzU = 110° %3D O mzR = 110°, mzT = 110°, m2U = 70° OM R = 110°, mzT = 70°, mzU = 110° m²R = 70°, mzT = 110°, m2U = 70° R %3D %3D %3D Mark this and return Save and Exit Next Submit

01:28:25 What are the missing angle measures in parallelogram 70° RSTU? mzR = 70°, mLT = 110°, mzU = 110° %3D O mzR = 110°, mzT = 110°, m2U = 70° OM R = 110°, mzT = 70°, mzU = 110° m²R = 70°, mzT = 110°, m2U = 70° R %3D %3D %3D Mark this and return Save and Exit Next Submit

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Determining Missing Angles in a Parallelogram

In the image, we have the parallelogram RSTU with one angle measurement provided. The angle at vertex $ S $ is given as $ 70^\circ $.

#### Question:
**What are the missing angle measures in parallelogram RSTU?**

#### Answer Choices:
1. $ m \angle R = 70^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 110^\circ $
2. $ m \angle R = 110^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 70^\circ $
3. $ m \angle R = 110^\circ $, $ m \angle T = 70^\circ $, $ m \angle U = 110^\circ $
4. $ m \angle R = 70^\circ $, $ m \angle T = 110^\circ $, $ m \angle U = 70^\circ $

#### Diagram Explanation:
The parallelogram RSTU is depicted with:
- $ S $ positioned at the bottom left,
- $ R $ at the bottom right,
- $ T $ at the top right, and
- $ U $ at the top left.

The image indicates angle measurement at:
- $ m \angle S = 70^\circ $.

#### Analyzing Angles in Parallelograms:
In a parallelogram:
1. Opposite angles are equal.
2. Consecutive angles are supplementary, meaning they add up to $ 180^\circ $.

Given $ m \angle S = 70^\circ $:
- $ m \angle R $, opposite to $ m \angle S $, also equals $ 70^\circ $.
- Consecutive angles $ m \angle T $ and $ m \angle U $:
- $ m \angle T = 180^\circ - 70^\circ = 110^\circ $
- $ m \angle U = 110^\circ $

Therefore, the correct angle measures are:
- $ m \angle R = 70^\circ $,
- $ m \angle T = 110^\circ $,
- $ m \angle U = 110^\circ $.

Thus, the correct answer

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