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Chapter 3: Q30 (page 99)

Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 8 and 12 respectively.

Step by step solution

01

Step 1. Description of step.

If two parallel lines are intersected by a transversal then alternate interior angles are congruent. Therefore,

2x+y=5x鈭�y5x鈭�2x鈭�y鈭�y=03x鈭�2y=0

02

Step 2. Apply an angle sum theorem.

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

100+2x+y+5x+y=1807x+2y=180鈭�1007x+2y=80

03

Step 3. Description of step.

Add equations obtained in step 1 and step 2 and simplify to find the value of x.


04

Step 4. Description of step.

Substitute 8 for xinto 3x鈭�2y=0to find the value of y.

role="math" 3脳8鈭�2y=024鈭�2y=0

role="math" localid="1638187017881" 2y2=242y=12

Therefore, the value of x and y is 8 and 12 respectively.

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