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Chapter 4: Q29. (page 139)

Find the values of x and y.

29. In 螖JKL,JK炉鈮�KL炉,m鈭�J=2x-y,m鈭�K=2x+2yandm鈭�L=x+2y

Short Answer

Expert verified

The value ofx andy is 30and 10 respectively.

Step by step solution

01

– Apply isosceles triangle theorem.

If the two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

In 螖JKL,JK炉鈮�KL炉implies that m鈭�J=m鈭�L.

02

– Description of step.

Substitute2x鈭�y form鈭�J andx+2y form鈭�L intom鈭�J=m鈭�L and simplify.

2x鈭�y=x+2yx=3y

03

– Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is 180.

Therefore,

m鈭�J+m鈭�K+m鈭�L=1802x鈭�y+2x+2y+x+2y=1805x+3y=180

04

– Description of step.

Substitute3y forx into5x+3y=180 to find the value of role="math" localid="1648815869555" x.

5(3y)+3y=18015y+3y=18018y=180y=10

05

– Description of step.

Substitute 10 fory into x=3y, to find the value of x.

x=3脳10=30

Therefore, the value ofx andy is 30 and 10 respectively.

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