### Exercise: Exterior and Interior Angles of Triangles---#### Problem 2:**Task**: Name the exterior angles shown in Fig. 13.23 and find the size of each exterior angle.**Diagram Explanation**:- **Figure 13.23**: The diagram is a triangle QAR with: - $\angle ABQ = 45^\circ$ - $\angle BCR = 60^\circ$---#### Problem 3:**Task**: Find the size of each of the lettered angles in Fig. 13.24.**Figure 13.24**: The diagram contains four different triangles, each with angles marked, some of which have letters representing unknown angles.- **Part a**: - $ \angle A = 35^\circ $ - $ \angle B = 100^\circ $ - $ \angle C = 18^\circ $ - Unknown angles: $ \angle x^\circ $ and $ \angle y^\circ $- **Part b**: - $ \angle A = 70^\circ $ - $ \angle B = 30^\circ $ - Unknown angles: $ \angle a^\circ $, $ \angle b^\circ $, and $ \angle c^\circ $- **Part c**: - $ \angle A = 115^\circ $ - $ \angle B = 31^\circ $ - Unknown angles: $ \angle h^\circ $ and $ \angle k^\circ $- **Part d**: - $ \angle A = 38^\circ $ - $ \angle B = 85^\circ $ - $ \angle C = 150^\circ $ - Unknown angles: $ \angle g^\circ $ and $ \angle l^\circ $---**Instructions**:1. **Identify the exterior angles**: Use the known interior angles to calculate the corresponding exterior angles. Remember that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.2. **Calculate each unknown angle**: Apply the angle sum property of triangles, which states that the sum of the interior angles of a triangle is $180^\circ$. **Note**: Carefully follow each step and ensure calculations are accurate for precise

As per the guidelines,we are suppose to answer only first question. Please repost again to get the…

Name the exterior angles shown in Fig. 13.23 and find the size of each DCP - 163°. exterior angle. 45 B 60 163 Fig. 13.23 D. 3. Find the size of each of the lettered angles in Fig. 13.24. a) 35 right line) 100° y° 18 b) of a A) 70 A 30° c) 4704 115 31 85 d) 38 150 FREE Name AtAl

Name the exterior angles shown in Fig. 13.23 and find the size of each DCP - 163°. exterior angle. 45 B 60 163 Fig. 13.23 D. 3. Find the size of each of the lettered angles in Fig. 13.24. a) 35 right line) 100° y° 18 b) of a A) 70 A 30° c) 4704 115 31 85 d) 38 150 FREE Name AtAl

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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### Exercise: Exterior and Interior Angles of Triangles

---

#### Problem 2:
**Task**: Name the exterior angles shown in Fig. 13.23 and find the size of each exterior angle.

**Diagram Explanation**:
- **Figure 13.23**: The diagram is a triangle QAR with:
- $\angle ABQ = 45^\circ$
- $\angle BCR = 60^\circ$

---

#### Problem 3:
**Task**: Find the size of each of the lettered angles in Fig. 13.24.

**Figure 13.24**: The diagram contains four different triangles, each with angles marked, some of which have letters representing unknown angles.

- **Part a**:
- $ \angle A = 35^\circ $
- $ \angle B = 100^\circ $
- $ \angle C = 18^\circ $
- Unknown angles: $ \angle x^\circ $ and $ \angle y^\circ $

- **Part b**:
- $ \angle A = 70^\circ $
- $ \angle B = 30^\circ $
- Unknown angles: $ \angle a^\circ $, $ \angle b^\circ $, and $ \angle c^\circ $

- **Part c**:
- $ \angle A = 115^\circ $
- $ \angle B = 31^\circ $
- Unknown angles: $ \angle h^\circ $ and $ \angle k^\circ $

- **Part d**:
- $ \angle A = 38^\circ $
- $ \angle B = 85^\circ $
- $ \angle C = 150^\circ $
- Unknown angles: $ \angle g^\circ $ and $ \angle l^\circ $

---

**Instructions**:
1. **Identify the exterior angles**: Use the known interior angles to calculate the corresponding exterior angles. Remember that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
2. **Calculate each unknown angle**: Apply the angle sum property of triangles, which states that the sum of the interior angles of a triangle is $180^\circ$.

**Note**: Carefully follow each step and ensure calculations are accurate for precise

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