Of the three angles of a triangle are equal and the third angle is greater than each one of them by 18°. Find the angle.

Question

Of the three angles of a triangle are equal and the third angle is greater than each one of them by 18&#xB0;. Find the angle.

Philoid · Accepted Answer

54°, 54°, 72°

Let ∠P, ∠Q and ∠R are three angles of triangle PQR,

And ∠P = ∠Q = a ________________ (i)

Then, ∠R = a + 18°________________ (ii)

We know that sum of angles of triangle = 180°

∠P + ∠Q + ∠R = 180° [Sum of angles]

⇒ a + a + a + 18°= 180° [From equation (i) and (ii)]

⇒ 3a= 162°

⇒ a= 54°

Therefore,

∠P = ∠Q =54° [from equation (i)]

∠R = 54° + 18° [from equation (i)]

= 72°