Two angles are supplementary. ∠QRS=x+40° and ∠SRT=x°. What is the value of ∠QRS?
70°
25°
110°
180°
110°
To find the value of ∠QRS, we need to recall that supplementary angles add up to 180 degrees. So, ∠QRS + ∠SRT = 180°.
Given that ∠QRS = x + 40° and ∠SRT = x°, we can substitute these values into the equation and solve for x:
(x + 40°) + x° = 180°
Combining like terms:
2x + 40° = 180°
Next, we isolate the term with x by subtracting 40° from both sides of the equation:
2x = 180° - 40°
Simplifying:
2x = 140°
Finally, we divide both sides of the equation by 2 to solve for x:
x = 140° / 2
x = 70°
Therefore, the value of ∠QRS is x + 40°, which means ∠QRS = 70° + 40° = 110°.
Hence, the correct answer is 110°.