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Chapter 3: Q21. (page 114)

In the diagram AB↔bisects role="math" localid="1647664217291" ∠DHF, AB↔⊥GH¯, AB↔∥CD↔, and m∠AHB=60°. Find the measure of each angle.

∠HDC.

Short Answer

Expert verified

The angle∠HDCis 60°.

Step by step solution

01

Step 1. Observe the diagram.

Here, ∠AHD=60°, AB↔⊥GH¯, AB↔∥CD↔ and AB↔ bisects ∠DHF .

02

Step 2. Show the calculation.

From the figure and the data,

As, AB↔∥CD↔, AB↔∥CE↔.

(As CE↔is the extended part of CD↔)

Take HD↔as a transversal.

Use the fact that if a transversal intersects two parallel lines, then alternate interior angles are equal.

So,

∠HDC=∠AHD=60°

Hence the angle∠HDC=60°.

03

Step 3. State the conclusion.

Therefore, ∠HDC=60°.

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Most popular questions from this chapter

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name four lines that appear to be skew toAB¯.

Write proof in two column form

Given: k∥l

Prove: ∠2≅∠7

Find the values xof yand

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

and

Use two lines of notebook paper as parallel lines and draw any

transversal. Use a protractor to measure

Measure one pair of alternate interior angles. Repeat the experiment with another transversal. What appears to be true?
See all solutions

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