Question

1. 10) 11) 12) 13) 14) 15) 16)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Also, vertical angles are equal.

Step2: Solve problem 9

For the triangle with known angles 20° and 40°, the third - angle is 180°-(20° + 40°)=120°. The angle opposite this (vertical angle) in the other triangle is also 120°. Then the unknown angle in the upper - triangle is 180°-(39° + 120°)=21°.

Step3: Solve problem 10

In the left - triangle, the third angle is 180°-(65° + 60°)=55°. The non - shared angle between the two triangles is 50°. In the right - triangle, the unknown angle is 180°-(35°+(55° + 50°))=40°.

Step4: Solve problem 11

In the right - triangle, the third angle is 180°-(84° + 36°)=60°. The unknown angle in the left - triangle is 180°-(86° + 60°)=34°.

Step5: Solve problem 12

For the triangle with known angles 35° and 23°, the third - angle is 180°-(35° + 23°)=122°. The angle opposite this (vertical angle) in the other triangle is also 122°. Then the unknown angle in the upper - triangle is 180°-(27° + 122°)=31°.

Step6: Solve problem 13

The sum of the interior angles of the polygon formed by the two triangles (excluding the right - angle) is 360°-(115° + 85°)=160°. The unknown angle outside the polygon is 180°-(160° + 90°+155° - 360°)=35°.

Step7: Solve problem 14

For the triangle with known angles 20° and 35°, the third - angle is 180°-(20° + 35°)=125°. The angle opposite this (vertical angle) in the other triangle is also 125°. The unknown angle in the upper - triangle is 180°-(125°+(180° - 156°))=71°.

Step8: Solve problem 15

In the left - triangle, the third angle is 180°-(60° + 45°)=75°. The non - shared angle between the two triangles is 68°. In the right - triangle, the unknown angle is 180°-(100°+(75° + 68° - 180°))=77°.

Step9: Solve problem 16

In the left - triangle, the third angle is 180°-(45° + 75°)=60°. The non - shared angle between the two triangles is 79°. In the right - triangle, the unknown angle is 180°-(68°+(60° + 79° - 180°))=73°.

Answer:

1. 21°
2. 40°
3. 34°
4. 31°
5. 35°
6. 71°
7. 77°
8. 73°