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Chapter 3: Q19 (page 98)

The largest two angles of a triangle are two and three times as large as the smallest angle. Find all three measures.

Short Answer

Expert verified

The measures of angles of triangle are, 30掳,60掳and 90掳.

Step by step solution

01

Step 1. Description of a step.

Let the smallest angle be x. Therefore, the other angles of a triangle, are 2x and 3x.

02

Step 2. Apply an angle sum theorem.

Consider a triangle, such that,

x+2x+3x=1806x=180x=30

03

Step 3. Description of a step.

Substitute 30 for x into x to find the measure of first angle.

Therefore, the value of x is

x=30

04

Step 4. Description of a step.

Substitute 30 for x into 2x to find the measure of second angle.

2x=2脳30=60

05

Step 5. Description of a step.

Substitute 30 for x into 3x to find the measure of third angle.

3x=3脳30=90

Therefore, the measures of angles of triangle are, 30掳,60掳and 90掳.

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