the measure of one angle of a right triangle is 38 degrees more than the measure of the smallest angle. find the measures of all three angles.

26°, 64°, 90° all three angles of right angle triangle.

Step-by-step explanation:

Given : the measure of one angle of a right triangle is 38 degrees more than the measure of the smallest angle.

To find : find the measures of all three angles.

Solution : We have given a right angle triangle

We know that in right angle one angle = 90 °.

Let the smaller angle = x.

According to question:

Other angle = 38 + x

By the angle sum property of triangle: sum of all angle is 180°.

x + 38 + x + 90 = 180.

2x + 38 + 90 = 180.

2x + 128 = 180.

On subtracting both sides by 128.

2x = 180 - 128.

2x = 52

On dividing both sides by 2.

x = 26.

Smaller angle = 26

second angle 26 + 38 = 64

Third angle = 90.

90 + 64 + 26 = 180.

Therefore, 26°, 64°, 90° all three angles of right angle triangle.