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Chapter 4: Q11. (page 165)

Find the measure of each numbered angle.

Short Answer

Expert verified

The angles are:

m∠5=90∘m∠6=54∘m∠7=36∘m∠8=54∘

Step by step solution

01

- Consider the diagram. 

Here, AB∥CD.

02

- Show the calculation.

Since, AB∥CD,

Here, m∠5=m∠F=90°, since they are corresponding angles, where FE is the transversal and AB is parallel to CD.

m∠5+m∠6+m∠GEC=180° …… [linear angles]

That implies,

m∠6+90∘+36∘=180∘m∠6+126∘=180∘

Subtract 126° from each side, then,

m∠6=180∘−126∘m∠6=54∘

Now, m∠7=m∠6=36°, since they are vertically opposite angles, where GE is the transversal and AB is parallel to CD.

And m∠8=m∠GEC=54°, since they are vertically opposite angles, where GE is the transversal and AB is parallel to CD.

03

- State the conclusion.

Therefore,

m∠5=90∘m∠6=54∘m∠7=36∘m∠8=54∘

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Most popular questions from this chapter

Plot the given points on graph paper. Draw ΔABCand ΔDEF. Copy and complete the statement role="math" localid="1638345245002" ΔABC≅?¯.

A1,1B8,1

D3,−7E5,−3F3,0

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Plot the given points on graph paper. Draw ΔABCand ΔDEF. Copy and complete the statement ΔABC≅?¯.

A−7,−3B−2,−3C−2,0

D0,1E5,1F0,−2

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

Copy and complete the proof.

1. Given: ∠P≅∠S;Ois the midpoint of PS¯. Prove: is the midpoint of RQ¯

Proof
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