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Chapter 10: Q.20 (page 540)

The ratio of the angle of a triangle is7:16:22. Find the angle measures. Then classify the triangle by its angle measures.

Short Answer

Expert verified

The angles measures are 28,鈭�64,鈭�88掳 respectively and the triangle is a scalene triangle.

Step by step solution

01

Step 1. Given Information.

The ratio of angles of a triangle is7:16:22.

02

Step 2. Calculation.

Let the angle measures be 7x, 16x, 22x.

Sum of all angles of a triangle is180掳.Hence,

7x+16x+22x=180掳

Add all the x on the left side of the equation.

45x=180掳

Divide both the sides by 45.

45x45=180掳45

This will give the value ofx=4.

Hence the angle measures are:

First angle is 7x, multiply 7 with 4.

7x=7脳4=28

Second angle 16x, multiply 16 with 4.

16x=16脳4=64

Third angle is 22x, multiply 22 with 4.

22x=22脳4=88

As all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is scalene triangle.

03

Step 3. Conclusion.

The angle measures of the triangle are and the triangle can be classified as scalene triangle.

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Most popular questions from this chapter

How are a trapezoid and a parallelogram different from each other.

Find the unknown base or height of the parallelogram.

A=40in.2,b=25in.,h=?炉

Find the unknown side length of the triangle given the perimeter P. Then classify the triangle by its side lengths.

P=84.3cm

Find the value of x.

Find the unknown base or height of the trapezoid.

A=240m2,b1=16m,b2=8m,h=?炉
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