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Chapter 3: Q. 3.76 (page 360)

The measure of one angle of a right triangle is 30掳 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掳,60掳,90掳.

Step by step solution

01

Step 1. Given information

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

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

Let the measure of second angle be x掳

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

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掳which means

x掳+(x+30)掳+90掳=180掳

On solving,

x+x+30=902x=90-302x=60x=30掳

03

Step 3. Find the measure of all angles.

As x=30掳then

x+30=60掳

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

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