Question

Points A, B, C and D are on the circle. The ∠ACB and ∠ADB are angles subtended by the same arc AB. If arc AB measures (5x – 30)° and m∠ACB = (x + 15) °, what is m∠ADB?

Answer 1

m∠ADB = 35°

Explanation:

From the figure attached,

∠ACB and ∠ADB are the angles subtended by the same arc AB.

m(arc AB) = (5x - 30)°

m∠ACB = (x + 15)°

Since, "measure of an arc is double of the measure of the angle subtended by the arc at the circumference"

m(arc AB) = 2(m∠ACB)

(5x - 30) = 2(x + 15)

5x - 30 = 2x + 30

5x - 2x = 30 + 30

3x = 60

x = 20

By using theorem,

"Angles subtended by the same arc in the same segment of a circle are equal in measure"

Therefore, m∠ACB = m∠ADB

Since, m∠ACB = (x + 15)°

= 20 + 15

= 35°

m∠ADB = 35°