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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°.

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

Therefore, the value of x can be obtained as:

8x−6+42=1808x+36=1808x=180−368x=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°and42° 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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Most popular questions from this chapter

PQRS is a parallelogram. Find the values of a, b, x and y.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD¯∥BC¯

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD; W, X, Y, Z are midpoints of AO¯, BO¯, CO¯and DO¯.

Prove: role="math" localid="1637745814874" WXYZ is a parallelogram.

Prove: If a segment whose endpoints lie on opposite sides of a parallelogram passes though the midpoint of a diagonal, that segment is bisected by the diagonal.

The legs of this ironing board are built so that BO=AO=RO=DO.

What theorem guarantees that the board is parallel to the floor AR¯∥BD¯?
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