### Educational Content: Triangle Angle Relationships#### Diagram ExplanationThe diagram shows a triangle with angles labeled as ∠1, ∠2, and an exterior angle labeled as ∠3. There is also an angle ∠4 on the extension of the side opposite to ∠2. #### QuestionsYou are asked to determine which of the following statements about the triangle's angles are true. Select all that apply:A. ∠1 + ∠2 = ∠3 + ∠4 B. ∠1 + ∠2 + ∠3 = 180° C. ∠1 + ∠2 = ∠4 D. ∠2 + ∠3 = ∠4 E. ∠1 + ∠2 + ∠3 + ∠4 = 180° Consider properties of triangles and exterior angles when responding to the above statements.

Answered: Which of the facts below are true for…

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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### Educational Content: Triangle Angle Relationships

#### Diagram Explanation
The diagram shows a triangle with angles labeled as ∠1, ∠2, and an exterior angle labeled as ∠3. There is also an angle ∠4 on the extension of the side opposite to ∠2.

#### Questions
You are asked to determine which of the following statements about the triangle's angles are true. Select all that apply:

A. ∠1 + ∠2 = ∠3 + ∠4
B. ∠1 + ∠2 + ∠3 = 180°
C. ∠1 + ∠2 = ∠4
D. ∠2 + ∠3 = ∠4
E. ∠1 + ∠2 + ∠3 + ∠4 = 180°

Consider properties of triangles and exterior angles when responding to the above statements.

Expert Solution

Step 1

In the given triangle $∠ 1, ∠ 2 and ∠ 3$ are its interior angles and $∠ 4$ is its exterior angle.

The sum of the all interior angles of a triangle is always $180^{\circ}$ .

Therefore, $∠ 1 + ∠ 2 + ∠ 3 = 180^{\circ}$

Thus, option B is correct.

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Which of the facts below are true for this triangle? Select all that apply. 2 1 3, A.O 21 + 22 = Z3 + Z4 Z1 + 22 + Z3 = 180° В. c.O Z1 + 22 = Z4 D.O 22 + Z3 = 24 Z1 + 22 + 23 + Z4 = 180° E.