The values of the numbered angles are
1. 41⁰
2. 85⁰
3. 95⁰
4. 85⁰
5. 36⁰
6. 49⁰
7. 106⁰
How the values of the angles are determined
From the figure
Angle3 = 95⁰(vertical angles)
Angle2 + angle3 = 180(supplementary angles)
Angle2 = 180 - 95
= 85⁰
Angle2 = angle4(vertical angles)
Angle4 = 85⁰
Angle5 + 144 = 180(supplementary angles)
Angle5 = 180 - 144
= 36⁰
Angle5 + angle6 + angle3 = 180(sum of angle in triangle)
36 + 95 + angle6 = 180
angle6 = 180 - 131
= 49⁰
angle6 + angle1 + 90 = 180(angles in a triangle)
49 +90 + angle1 = 180
angle1 = 180 - 139
= 41⁰
Angle5 + angle7 + 38 = 180(angles in a triangle)
angle7 = 180 - 38 - 36
angle7 = 106⁰