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Chapter 5: Q22 (page 170)

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 65 and 20 respectively.

Step by step solution

01

Step 1. Description of step.

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

Consider 螖AOD, such that,

m鈭�AOD+m鈭�ADO+m鈭�DAO=180m鈭�AOD+x鈭�y+x+y=180m鈭�AOD+2x=180m鈭�AOD=180鈭�2x

02

Step 2. Description of step.

From the given figure,

m鈭�AOD+m鈭�DOC=180m鈭�AOD+130=180m鈭�AOD=50掳

03

Step 3. Description of step.

Substitute 50 for m鈭�AODinto m鈭�AOD=180鈭�2x to find the value of x.

50=180鈭�2x2x=180鈭�502x=130x=65

04

Step 4. Alternate interior angles.

From the figure, it can be observed that, AD炉鈭�BC炉, AC炉is a transversal and 鈭�DAC,鈭�ACBare alternate interior angles such that

m鈭�DAC=m鈭�ACBx+y=85

05

Step 5. Description of step.

Substitute 65 for x into x+y=85 to find the value of y.

65+y=85y=85鈭�65=20

Therefore, the value of x and y is 65 and 20 respectively.

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Most popular questions from this chapter

In Exercise 5 quad. ABCD is a parallelogram. Find the values of x, y, and z.

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.

For the following figure, if RE=EWthen name all angles congruent to 鈭�ERW.

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.

Given: ABCDis a 鈻�,鈭�A鈮�鈭�E

Prove: localid="1637661691185" AB炉鈮�CE炉
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