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Chapter 3: Q22. (page 114)

In the diagram AB鈫� bisects 鈭�DHF, AB鈫�鈯�GH炉, AB鈫�鈭�CD鈫�, and role="math" localid="1647713022816" m鈭�AHB=60掳. Find the measure of each angle.

鈭�HCD

Short Answer

Expert verified

The angle鈭�HCDis 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,

鈭�BHCand 鈭�AHFare vertical angles and they are congruent.

鈭�BHC=鈭�AHF=60掳

鈭�BHCand 鈭�AHFare alternate angles and they are congruent.

鈭�BHC=鈭�HCD=60掳

Hence the angle 鈭�HCD=60掳.

03

Step 3. State the conclusion.

Therefore, 鈭�HCD=60掳.

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