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Chapter 5: Q7 (page 169)

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

Short Answer

Expert verified

The values of a, b, x and y are 5,3,120掳and 22掳respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

02

Step 2. Description of step.

In the given figure, PS炉鈮�QR炉implies that a=5and PQ炉鈮�SR炉implies that b=3.

03

Step 3. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

04

Step 4. Description of step.

From the given figure, it can be observed that 鈭�x鈮�鈭�PSRimplies that

x=m鈭�PSR=120掳

05

Step 5. Description of step.

Consider 螖PQR,

The sum of measures of all angles of a triangle is 180. Therefore,

m鈭�QPR+m鈭�PQR+m鈭�QRP=18038+120+m鈭�QRP=180m鈭�QRP=180鈭�158=22掳

06

Step 6. Description of step.

Both pairs of opposite sides of a parallelogram are parallel, that is, PS炉||QR炉and SQ炉is a transversal then angle made by a transversal with respect to two lines are equal.

鈭�SPR鈮�鈭�QRP

Therefore,

m鈭�SPR=m鈭�QRP=22掳x=22掳

Therefore, the values of a, b, x and y are 5,3,120掳and 22掳respectively.

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Most popular questions from this chapter

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

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

M, N and T are the midpoints of the sides of 螖XYZ.

State the theorem suggested by Exercise 6.

Prove Theorem 5-1.

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(-1,0),(2,-2),(2,2)
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