Question

I need help on this question

Answer 1

Answer

Arc EF = 52°

Arc HD = 142°

Angle HGF = 128°

Explanation

To solve for the unknown angles, we need to first solve for x

To do that, we need to first note that the sum of angles on a straight line is 180°

So,

Angle HCG + Angle HCD = 180° (Sum of angles on a straight line)

Angle HCG = 2x

Angle HCD = 6x + 28°

Angle HCG + Angle HCD = 180°

2x + 6x + 28° = 180°

8x + 28° = 180°

8x = 180° - 28°

8x = 152°

Divide both sides by 8

(8x/8) = (152°/8)

x = 19°

Angle HCG = 2x = 2 (19°) = 38°

Angle HCD = 6x + 28° = 6(19°) + 28° = 142°

So, we can solve for the rest now

Arc EF = Angle ECF

= 90° - Angle ECD

Angle ECD = Angle HCG = 38° (Vertically opposite angles are equal)

Arc EF = Angle ECF

= 90° - Angle ECD

= 90° - 38°

= 52°

Arc HD = Angle HCD = 142°

Angle HGF = Angle HCG + Angle GCF = 38° + 90° = 128°

Hope this Helps!!!