Answer:
a) Angle 1 = Value in degree = 95°
b)Angle 2 = Value in degree = 77°
c) Angle 3 = Value in degree = 85°
d) Angle 4 = Value in degree = 103°
Explanation:
We use circle theorems to solve for this above question.
a) Angle 1 = Value in degree = 95°
Inscribed Angle is 1/2 of an Intercepted Arc
From the diagram, Angle 1 intersects at Arc B and Arc C
This means Angle 1 = (B + C)/ 2 =
Arc B = 100°
Arc C = 90°
Angle 1. = (100° + 90°)/ 2 = 190/ 2 = 95°
b)Angle 2 = Value in degree = 77°
From the diagram, Angle 2 intersects at Arc C and Arc D
Inscribed Angle is 1/2 of an Intercepted Arc
This means Angle 1 = (C+ D)/ 2
C = 90°
D = 64°
Angle 1. = (90° + 64°)/ 2 = 154/ 2 = 77°
c) Angle 3 = Value in degree = 85°
From the diagram, we can see that Angle 1 is opposite Angle 3, hence,
Opposite angles are supplementary which means their addition = 180°
Mathematically:.Angle 1 + Angle 3 = 180°
Angle 1 = 95°
95° + Angle 3 = 180°
Angle 3 = 180° - 95° = 85°
d) Angle 4 = Value in degree = 103°
From the diagram, we can see that Angle 2 is opposite Angle 4,
Hence,
Opposite angles are supplementary which means their addition = 180°
Mathematically:.Angle 2 + Angle 4 = 180°
Angle 2 = 77°
77° + Angle 3 = 180°
Angle 4 = 180° - 77° = 103°