The larger of two supplementary angles is 50° more than the smaller one. The smaller angle (in degrees) is: 1. 65° 2. 67°
Answer (1)
To solve this problem, we need to understand that supplementary angles are two angles whose sum is 180 degrees.
Let's denote the smaller angle as x degrees. According to the problem, the larger angle is 50 degrees more than the smaller angle, so we can represent it as x + 50 degrees.
Since these angles are supplementary, their sum should be 180 degrees. Therefore, we can set up the equation:
x + ( x + 50 ) = 180
Simplifying this equation:
2 x + 50 = 180
Subtract 50 from both sides to isolate terms involving x :
2 x = 130
Next, divide both sides by 2 to solve for x :
x = 65
Therefore, the smaller angle is 65 degrees.
So, the correct choice is:
65 ∘
