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Chapter 3: Q21. (page 114)

In the diagram AB鈫�bisects role="math" localid="1647664217291" 鈭�DHF, AB鈫�鈯�GH炉, AB鈫�鈭�CD鈫�, and m鈭�AHB=60掳. Find the measure of each angle.

鈭�HDC.

Short Answer

Expert verified

The angle鈭�HDCis 60掳.

Step by step solution

01

Step 1. Observe the diagram.

Here, 鈭�AHD=60掳, AB鈫�鈯�GH炉, AB鈫�鈭�CD鈫� and AB鈫� bisects 鈭�DHF .

02

Step 2. Show the calculation.

From the figure and the data,

As, AB鈫�鈭�CD鈫�, AB鈫�鈭�CE鈫�.

(As CE鈫�is the extended part of CD鈫�)

Take HD鈫�as a transversal.

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

So,

鈭�HDC=鈭�AHD=60掳

Hence the angle鈭�HDC=60掳.

03

Step 3. State the conclusion.

Therefore, 鈭�HDC=60掳.

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