The difference between the two angles formed at the intersection of two straight lines is 116 degrees, find these angles.
August 18, 2021 | education
| 1. Let’s denote the degree measure of the smaller angle through x.
2. Determine the degree measure of the larger angle:
(x + 116˚)
3. Since the sum of adjacent angles is 180˚, we compose and solve the equation:
(x + 116˚) + x = 180˚;
x + 116˚ + x = 180˚;
2x + 116˚ = 180˚;
2x = 180˚ – 116˚;
2x = 64˚;
x = 64˚: 2;
x = 32˚.
4. The degree measure of the smaller angle is x = 32˚.
5. What is the degree measure of the larger angle?
x + 116˚ = 32˚ + 116˚ = 148˚.
Answer: the degree measures of the angles formed at the intersection of two straight lines are equal to 148˚ and 32˚.
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