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Chapter 2: Q. 2.66 (page 136)

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

30掳,60掳,90掳are the measures of all three angles.

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 have to find the measures of all three angles.

02

Step 2. Name. 

Choose a variable to represent it.

Leta=1stangle.a+30掳=2ndangle90掳=3rdangle(therightangle)

Draw the figure and label it with the given information.

03

Step 3. Translate. 

Write the appropriate formula.

m鈭�A+m鈭�B+m鈭�C=180掳

Substitute into the formula.

a+(a+30掳)+90掳=180掳

04

Step 4. Solve the equation

a+(a+30掳)+90掳=180掳2a+120掳=180掳2a=180掳-120掳2a=60掳a=30掳firstanglea+30掳secondangle30掳+30掳=60掳90掳thirdangle

05

Step 5. Check

30掳+60掳+90掳=180掳180掳=180掳verified

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