The difference between the two angles formed at the intersection of two straight lines is 42 degrees. Find all the angles formed.
August 30, 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 + 42˚)
3. Since the sum of adjacent angles is 180˚, we compose and solve the equation:
(x + 42˚) + x = 180˚;
x + 42˚ + x = 180˚;
2x + 42˚ = 180˚;
2x = 180˚ – 42˚;
2x = 138˚;
x = 138˚: 2;
x = 69˚.
4. The degree measure of the smaller angle is x = 69˚.
5. What is the degree measure of the larger angle?
x + 42˚ = 69˚ + 42˚ = 111˚.
6. As you know, the vertical angles are equal, so the large angles formed at the intersection of two straight lines will be equal to 111˚, and the smaller angles will be equal to 69˚.
Answer: the degree measures of the angles formed at the intersection of two straight lines are equal to 111˚, 69˚, 111˚, 69˚.
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