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Chapter 3: Q. 3.76 (page 360)

The measure of one angle of a right triangle is 30° more than the measure of the smallest angle. Find the measures of all three angles.

Short Answer

Expert verified

The three angles of given right triangle are30°,60°,90°.

Step by step solution

01

Step 1. Given information

The measure of one angle of a right triangle is 30° more than the measure of the smallest angle.

We are given right triangle, so measure on angle will be 90°.

Let the measure of second angle be x°

then the measure of second angle will be(x+30)°.

02

Step 2. Use the angle sum property of the triangle.

We know that the sum of measure of all angle of a triangle is 180°which means

x°+(x+30)°+90°=180°

On solving,

x+x+30=902x=90-302x=60x=30°

03

Step 3. Find the measure of all angles.

As x=30°then

x+30=60°

So the measure of all angles of given right triangle is30°,60°,90°.

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