Question

A triangle ABC is inscribed in a circle, such that AB is a diameter. What are the measures of angles of this triangle if: measure of arc AC = 70°.

Answer 1

Part 1) The measure of angle C is 90°

Part 2) The measure of angle B is 35°

Part 3) The measure of angle A is 55°

Explanation:

we know that

The inscribed angle is half that of the arc it comprises.

step 1

Find the measure of angle C

The diameter divide the circle into two equal parts

so

If AB is a diameter

arc AB=180°

∠C=(1/2)[arc AB]

∠C=(1/2)[180°]=90°

step 2

Find the measure of angle B

arc AC=70°

∠B=(1/2)[arc AC]

∠B=(1/2)[70°]=35°

step 3

Find the measure of angle A

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

substitute

∠A+35°+90°=180°

∠A=180°-(35°+90°)

∠A=55°