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Chapter 5: Q19 (page 175)

What values must x and y have to make the quadrilateral a parallelogram?

Short Answer

Expert verified

The values that must x and y must have to make the quadrilateral a parallelogram are 18 and 14 respectively.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Find the value of x.

As the sum of the adjacent angles of the parallelogram is 180掳.

Therefore, to make the given quadrilateral a parallelogram, the sum of the adjacent angles measuring 8x鈭�6掳and42掳 should be 180掳.

Therefore, the value of x can be obtained as:

8x鈭�6+42=1808x+36=1808x=180鈭�368x=144x=1448x=18

Therefore, the value of x is 18.

03

Step 3. Find the value of y.

As the opposite angles of the parallelogram are congruent.

Therefore, to make the given quadrilateral a parallelogram, the opposite angles measuring 3y掳and42掳 should be equal.

Therefore, the value of y can be obtained as:

3y=42y=423y=14

Therefore, the value of y is 14.

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