Question

In a cyclic quadrilateral HDFC, angle H = 2x + 10 and angle F = 3x+20. Find angle H.

1)50°
2)90°
3)30°
4)70°​

Answer 1

Step-by-step explanation:

In cyclic quadrilateral, opposite angles sum up to 180°.

since angle H and angle F are opposite angles of quadrilateral HDFC.

=> angle H + angle F = 180°

=> 2x + 10 + 3x + 20 = 180°

=> 5x + 30 = 180°

=> 5x = 180° - 30°

=> 5x = 150°

=> x = 150°/5

=> x = 30°

Therefore, angle H = 2x + 10 = 2×30 +10

=> Angle H = 60+10

=> Angle H = 70°