Question

Suppose you know that

∠
S and
∠
Y are complementary, and that
m
∠
S = 3(m
∠
Y) − 110
°
. Find m
∠
Y.

Answer 1

The measure of angle Y is 50 degrees.

Step-by-step explanation:

To find the measure of angle Y, we can use the fact that angle S and angle Y are complementary, which means the sum of their measures is 90 degrees. We are also given that the measure of angle S is 3 times the measure of angle Y minus 110 degrees.

Let's set up the equation to represent these relationships: m∠S = 3(m∠Y) - 110° and m∠S + m∠Y = 90°.

Substituting the value of m∠S from the first equation into the second equation:

3(m∠Y) - 110° + m∠Y = 90°

Combining like terms:

4(m∠Y) - 110° = 90°

Adding 110° to both sides:

4(m∠Y) = 200°

Dividing both sides by 4:

m∠Y = 50°

Therefore, the measure of angle Y is 50 degrees.

Answer 2

x=36
y=17
L=15
M=75
N=55
P=35
N+P = 55+35 = 90 degrees: Complementary angles.