Two angles are supplementary. They have the following measures: m∠QRS=(x+16)° and m∠SRT=(3x)° . What is the measure of ∠SRT ?(1 point)

Answer 1

The sum of two supplementary angles is 180 degrees. So, we have the equation:

m∠QRS + m∠SRT = 180

Substituting the given measures of m∠QRS and m∠SRT, we get:

(x+16) + (3x) = 180

Simplifying the equation, we combine like terms:

4x + 16 = 180

Next, we isolate the variable term:

4x = 180 - 16
4x = 164

Finally, we solve for x by dividing both sides of the equation by 4:

x = 164/4
x = 41

Now, we can find the measure of ∠SRT by substituting the value of x:

m∠SRT = 3x = 3(41) = 123

Therefore, the measure of ∠SRT is 123 degrees.