Question

In an isosceles triangle, the 2nd angle is 20 more than half of one of the base angles. Find the measure of its three angles. ​

Answer 1

Let the base angles be x.

The second angle = 20 + 1/2 x

Sum of all angles is 180°

$(20 + \frac{ {1} }{2} x) + x + x = 180$

$20 + \frac{1}{2} x + x + x = 180$

$20 + \frac{1}{2} x + 2x = 180$

$20 + 2.5x = 180$

$2.5x = 180 - 20$

$2.5x = 160$

$x = \frac{160}{2.5}$

$x = 64$

The measure of base angles is 64°.

The measure of second angle =

$= 20 + \frac{1}{2} (64)$

$= 20 + 32$

$= 52$

The measure of second angle is 52°.