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Chapter 3: Q29 (page 99)

Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 25 and 5 respectively.

Step by step solution

01

Step 1. Apply exterior angle theorem.

The measure of exterior angle of a triangle is the sum of measure of two remote interior angles of a triangle.

From the given diagram it can be observed that,

x+2y+90=125x+2y=125−90x+2y=35x=35−2y

02

Step 2. Apply an angle sum theorem.

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

x+2y+90+2x+y=1803x+3y=180−903x+3y=90x+y=30

03

Step 3. Description of step.

Substitute 35−2y for x into the equation obtained in Step 2 to find the value of y.

35−2y+y=30−y=−5y=5

04

Step 4. Description of step.

Substitute 5 for y into the equation obtained in step 1 to find the value of x.

x=35−2×5=35−10

=25

Therefore, the value of x and y is 25 and 5 respectively.

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