Question

In ​ABC, angle B is one half the angle A and angle C is 15 less than the angle A. What are the measures of the angles of ​ABC?

Answer 1

∠A = 78° , ∠B = 39° and ∠C = 63°

Explanation:

Let the measure of angle A = m°

So, according to the question

Angle B = (m/2)°

Angle C = (m - 15)°

Now by ANGLE SUM PROPERTY, the sum pf all angles of a triangle is 180°

⇒ ∠A +∠B + ∠C = 180°

or, m + (m/2) + (m -15) = 180°

Solving for m , we get 2m + (m/2) = 180 + 15

or,
`(5m)/(2)  = 165\\or, m = 195 * (2)/(5)`

or, m = 78°

Hence ∠A = 78°

∠B = (m/2) = (78/2) = 39°

and ∠C = (m -15) = 78 - 15 = 63°