Question

The measure of one angle on a right triangle is 16° more than the measure of the smallest angle.

find the measures of all three angles

Answer 1

Answer: 37° 53° 90°

Explanation:

Given:

ΔABC m∠C=90°

Solution:

m∠A+m∠B+m∠C=180°

m∠A+m∠B+90°=180°

m∠A+m∠B+90°-90°=180°-90°

m∠A+m∠B=90°

Let m∠A=x°

Hence,

m∠B=(x+16)°

Thus,

x°+(x+16)°=90°

(2x)°+16°=90°

(2x)°+16°-16°=90°-16°

(2)(x)°=74°

Divide both parts of the equation by 2:

x°=m∠A=37°

m∠B=37°+16°

m∠B=53°