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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°,60°and 90°.

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=2×30=60

05

Step 5. Description of a step.

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

3x=3×30=90

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

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