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Chapter 3: Q11. CUR (page 114)

Draw a diagram that satisfies the conditions stated. If the conditions cannot be satisfied, write not possible.

QX鈫�bisects 鈭�PQR, m鈭�PQX=5x+13and m鈭�XQR=9x鈭�39 . Find (a) the values of x and (b) m鈭�PQR.

Short Answer

Expert verified

(a) The value of x is 13鈭�.

(b)m鈭�PQR=156鈭�

The diagram is:

Step by step solution

01

Part a. Step 1. Sketch the diagram.

QX鈫� bisects 鈭�PQR,m鈭�PQX=5x+13 and m鈭�XQR=9x+39.

Based on the information the diagram is:

02

Part a. Step 2. Show the calculation.

m鈭�PQX=m鈭�XQR5x+13=9x鈭�394x=52x=13鈭�

03

Part a. Step 3. State the conclusion.

Therefore, the value of x is 13鈭�.

04

Part b. Step 1. Sketch the diagram.

QX鈫�bisects 鈭�PQR, m鈭�PQX=5x+13and m鈭�XQR=9x+39.

Based on the information the diagram is:

05

Part b. Step 2. Show the calculation.

m鈭�PQR=m鈭�PQX+m鈭�XQR=5x+13+9x鈭�39=14x鈭�26

From subpart (a) x=13. Then,

m鈭�PQR=14x鈭�26=14脳13鈭�26=156

06

Part b. Step 3. State the conclusion.

Therefore,m鈭�PQR=156鈭�

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