Two angles are supplementary and have measures m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?(1 point) Responses 180° 180 degrees 110° 110 degrees 25° 25 degrees 70°
The sum of two supplementary angles is 180 degrees. Therefore, we have the equation:
m∠QRS + m∠SRT = 180
Substituting the given angle measures, we have:
(x + 40) + x = 180
Simplifying, we get:
2x + 40 = 180
Subtracting 40 from both sides:
2x = 140
Dividing both sides by 2:
x = 70
Therefore, the measure of ∠QRS is (x + 40) = 70 + 40 = 110 degrees.
The correct answer is 110°.