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Chapter 3: Q20. (page 114)

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

∠HDE.

Short Answer

Expert verified

The angle ∠HDE is 120°.

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 sum of each pair of co-interior angles is 180°.

So,

∠AHD+∠HDE=180°

Put ∠AHD=60°.

Then,

60∘+∠HDE=180∘∠HDE=180∘−60∘=120∘

Hence the angle ∠HDE=120°.

03

Step 3. State the conclusion.

Therefore, ∠HDE=120°.

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