Two angles are supplementary and have measures m∠QRS=(x+40)° and m∠SRT=x°. What is the measure of ∠QRS?(1 point) Responses 70° 70 degrees 180° 180 degrees 110° 110 degrees 25°
Since the two angles are supplementary, their measures add up to 180°.
So, we have the equation:
(x+40) + x = 180
Simplifying the equation:
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)°, which is equal to:
(70+40)° = 110°
So, the measure of ∠QRS is 110°.
Three angles measures add to 180° and have the following measures: m∠ACB=(x+15)° , m∠BCD=(x+48)°, and m∠DCE=13°. What is the measure of ∠BCD?(1 point) Responses 52° 52 degrees 67° 67 degrees 80° 80 degrees 100°
Since the three angles add up to 180°, we have the equation:
(x+15) + (x+48) + 13 = 180
Simplifying the equation:
2x + 76 + 13 = 180
Combining like terms:
2x + 89 = 180
Subtracting 89 from both sides:
2x = 91
Dividing both sides by 2:
x = 45.5
Therefore, the measure of ∠BCD is (x+48)°, which is equal to:
(45.5+48)° = 93.5°
So, the measure of ∠BCD is 93.5°.