One of the angles formed at the intersection of two straight lines is 90 degrees larger than the other. How many times is it larger than the other angle?
1. Let’s denote the degree measure of the second angle through x.
2. Let’s define the degree measure of the first angle:
(x + 90˚)
3. Since the sum of adjacent angles is 180˚, compose and solve the equation:
(x + 90˚) + x = 180˚;
x + 90˚ + x = 180˚;
2x + 90˚ = 180˚;
2x = 180˚ – 90˚;
2x = 90˚;
x = 90˚: 2;
x = 45˚.
4. The degree measure of the second angle is x = 45˚.
5. What is the degree measure of the first angle?
x + 90˚ = 45˚ + 90˚ = 135˚.
6. How many times is the first angle greater than the second angle?
135˚: 45˚ = 3.
Answer: the first corner is 3 times larger than the second corner.
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