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Chapter 5: Q2 (page 197)

In the following figure, a parallelogram EFGHis given and m鈭�EFG=70. If m鈭�EFH=32then find m鈭�EHF.

Short Answer

Expert verified

The measure of m鈭�EHF=38鈭�.

Step by step solution

01

Step 1. Apply the concept of a parallelogram.

In a parallelogram, the consecutive angles are supplementary.

02

Step 2. Check the figure.

Consider the figure.

03

Step 3. Step description.

Since the consecutive angles are supplementary therefore find the value of m鈭�HEFas follows:

m鈭�EFG+m鈭�HEF=180鈭�70鈭�+m鈭�HEF=180鈭�m鈭�HEF=180鈭�鈭�70鈭�m鈭�HEF=110鈭�

Now find m鈭�EHFas follows:

m鈭�EHF+m鈭�EFH+m鈭�HEF=180鈭�m鈭�EHF+32鈭�+110鈭�=180鈭�m鈭�EHF=180鈭�鈭�32鈭�鈭�110鈭�m鈭�EHF=38鈭�

Therefore, the measure is m鈭�EHF=38鈭�.

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Most popular questions from this chapter

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SA炉鈮�KC炉;SA炉鈭�KC炉

鈻�DECKis a parallelogram. Complete.

Ifm鈭�1=3x,m鈭�2=4x and m鈭�3=x2-70then x=?andm鈭�CED=? (numerical answers).

Give the reason for each step in the following proof of theorem 5-6

Given: m鈭�A=m鈭�C=x;m鈭�B=m鈭�D=y

Prove: ABCD is a parallelogram.

Proof:

In the exercise 3 quad.ABCD is a parallelogram. Find the values of x, y, and z.

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