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In the diagram ABbisects DHF, ABGH¯, ABCD, and mAHB=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°, ABGH¯, ABCD and AB bisects DHF .

02

Step 2. Show the calculation.

From the figure and the data,

As, ABCD, ABCE.

(As CEis the extended part of CD)

Take HDas 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=180HDE=18060=120

Hence the angle HDE=120°.

03

Step 3. State the conclusion.

Therefore, HDE=120°.

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