Question

What is the measure of (3y + 27) What is the measure of (5y - 3)

Answer 1

Answer:

The measure of (3y + 27) is 72

The measure of (5y - 3) is 72

Step-by-step explanation:                                                        

In a parallelogram, the opposite angles are congruent. Which means, ∠A and ∠C are congruent, and ∠B and ∠D are congruent. Therefore, when solving for y, you would write down: 3y+27 = 5y-3. Then, you would go ahead and solve for y. The work for solving for y will be included if you forget how or unsure how to solve for y.                            

After that, you would substitute the answer that you got for y where the y would be. As seen, the answer for y is 15. Therefore, you would put 3(15)+27= x. Same for the other problem, 5(15)-3= x.  Then you would solve for x. Basically, you would do 15 multiplied by 3= 45, then add 27 to 45, getting an answer of 72. For the next problem, you would do 15 multiplied by 5 equaling 75, then subtract 3 from 75, getting an answer of 72.              

Then, in order to solve for the measure of ∠B, you need to know this: the corresponding angles are supplementary. Corresponding angles are angles like ∠A and ∠B. They are basically angles right next to each other. In addition, when I say that corresponding angles are supplementary, that means that the sum of ∠A and ∠B equal 180°. Along with that, the sum of ∠B and ∠C= 180°. Also, the sum of ∠C and ∠D= 180°. Plus, the sum of ∠A and ∠D= 180°. Therefore, you would do 72+x= 180. X is being used as the variable for the measure of ∠B, since we are not sure what the measure of ∠B is. The work for this will also be included if you are unsure or forget how to solve for x.                          

Answer 2

Answer:

Angle A: 72°

Angle B: 108°

Step-by-step explanation:

Opposite angles are equal

Adjacent angles add up to 180

5y - 3 = 3y + 27

2y = 30

y = 15

Angle A:

5(15) - 3 = 72°

Angle B:

180 - 72 = 108°