Question

Someone help with this please​

Answer 1

I guess there is a small mistake in the options, as the correct answer is 130°, please first confirm all the options from your teacher.

Question :

Part of a roof is shaped like a parallelogram, as shown below. What is the measure of angle B?

• A. 50
• B. 40
• C. 20
• D. 18

Answer :

• ∠B = 130°.

Solution :

We have a parallelogram, ABCD, which have :

• BC = 18 ft.
• DC = 20 ft.
• ∠C = 50°

We have to find, ∠B.

First of all, we know that opposite angles of a parallelogram are equal.

=> ∠A = ∠C = 50° and ∠B = ∠D

Now, we know that sum of all angles of a parallelogram is 360°.

=> ∠A + ∠B + ∠C + ∠D = 360°

Now fill values of :

• ∠A = 50°
• ∠C = 50°
• ∠D = ∠B

=> 50° + ∠B + 50° + ∠B = 360°

=> 50° + 50° + ∠B + ∠B = 360°

=> 100° + 2∠B = 360°

=> 2∠B = 360° - 100°

=> 2∠B = 260°

=> ∠B = 260° ÷ 2

=> ∠B = 130°

Hence, ∠B = 130°.