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Chapter 5: Q13 (page 187)

Quad. STLM is a rhombus.

If m鈭�1=3x+1and m鈭�3=7x-11find the value of x.

Short Answer

Expert verified

The value of x is 10.

Step by step solution

01

Step 1. Description of step.

Diagonals of a rhombus bisect the vertex angles.

Here, 鈭�LSMis divided into 鈭�1and鈭�2, that is, m鈭�1=m鈭�2.

02

Step 2. Description of step.

Here, 鈭�SLTis divided into 鈭�3and鈭�4, that is, m鈭�3=m鈭�4.

03

Step 3. Description of step.

Here, 鈭�Sand鈭�Lare supplementary.

Substitute m鈭�3for m鈭�4and m鈭�1for m鈭�2 to find the value of x.

m鈭�1+m鈭�2+m鈭�3+m鈭�4=180m鈭�1+m鈭�1+m鈭�3+m鈭�3=1802m鈭�1+2m鈭�3=1802m鈭�1+m鈭�3=18023x+1+7x鈭�11=18020x鈭�1=180x鈭�1=9x=10

Therefore, the value of x is 10.

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Most popular questions from this chapter

For exercises, 14-18 write paragraph proofs.

Given: parallelogram KGLJ; FK=HL.

Prove: FGHJ is a parallelogram.

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

AD炉鈮�BC炉

Prove Theorem 5-1.

Quadrilateral is a parallelogram.

  1. Why is supplementary to ?
  2. Why is supplementary to ?
  3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

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

m鈭�ABC=m鈭�CDA
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