Question

Parallelogram ABCD is shown below. Parallelogram A B C D. Angle A is 104 degrees. Angle C is opposite to angle A. What is the measure of Angle B? 52Degrees A

76Degrees B

104Degrees C

152Degrees D

Answer 1

Answer:

B. 76°

Step-by-step explanation:

The theorem regarding the angles of parallelograms is that the two sets of opposite angles are congruent. This means that in this parallelogram:

∠A ≅ ∠C

∠B ≅ ∠D

We also know that the sum of all angles in a quadrilateral is equal to 360°.

Let's correlate these assumptions:

∠A + ∠B + ∠C + ∠D = 360°

∠A ≅ ∠C

∠B ≅ ∠D

So through substitution:

∠A + ∠B + ∠A + ∠B = 360°

2(∠A) + 2(∠B) = 360°

We are given:

m∠A = 104°

Now let's insert that in our equation:

2(∠A) + 2(∠B) = 360°

2(104°) + 2(∠B) = 360°

208° + 2(∠B) = 360°

Subtract 208° from both sides of the equation:

208° - 208° + 2(∠B) = 360°- 208°

2(∠B) = 152°

Divide both sides by 2:

2(∠B)/2 = 152°/2

∠B = 76°

Answer 2

Answer:

Try 76.....

Step-by-step explanation:

Hope it helps