Question

The answer choices apply for each letter answer. I just need a brief explanation with the answer

Answer 1

m∠a = 52º

m∠b = 128°

m∠r = 100º

m∠s = 100º

Step-by-step explanation:

m∠a and m∠b are supplementary angles. That means they add up to 180º.

So,

m∠a + m∠b = 180º

13y + 31y + 4= 180º

44y = 180 - 4

44y = 176

y = 4

m∠a = 13y = 13*4

m∠a = 52º

and

m∠b = 31y + 4

m∠b = 31*4 + 4

m∠b = 128º

Now, let's evaluate m∠r and m∠s. m∠r and m∠s are equal.

So,

m∠r = m∠s

30x + 40 = 130x - 160

40 + 160 = 130x - 30x

200 = 100x

200/100 = x

x = 2

So,

m∠r = 30x + 40 = 30*2 + 40

m∠r = 100º

And

m∠s = 130x - 160

m∠s = 130*2 - 160

m∠s = 260 - 160

m∠s = 100º

SummarizingThanks, and have a great day!,

m∠a = 52º

m∠b = 128°

m∠r = 100º

m∠s = 100º