Angles
Find the value of variables x and y.
1. x = 65
Based on the figure, since the two angles are congruent, let us equate it to each other.
Given angle measurements:
120°
(2x - 10)°
- 120 = 2x - 10
- 120 + 10 = 2x
- 130 = 2x
- 130/2 = x
- 65
Therefore, the value of x is 65. Let us check of the two angles are congruent.
- 120 = 2x - 10; x = 65
- 120 = 2(65) - 10
- 120 = 130 - 10
- 120 = 120
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2. x = 12
Based on the figure, the two angles formed a linear pair, so that means these two angles are supplementary. Let us equate it to 180.
Given angle measurements:
(2x)°
(4x + 108)°
- 2x + 4x + 108 = 180
- 6x + 108 = 180
- 6x = 180 - 108
- 6x = 72
- x = 72/6
- x = 12
Therefore, the value of x is 12. Let us check if the two angles are supplementary.
- 2x + 4x + 108 = 180; x = 12
- 2(12) + 4(12) + 108 = 180
- 24 + 48 + 108 = 180
- 72 + 108 = 180
- 180 = 180
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3. x = 15, y = 145
Based on the figure, we need to find the value of x before we determine for the value of y. Since the two angles that has the variable x is congruent, therefore we will equate it to each other.
Given angle measurements (the variable x):
(2x + 5)°
(3x - 10)°
- 2x + 5 = 3x - 10
- 2x - 3x = -5 - 10
- -x = -15
- x = -15/-1
- x = 15
Therefore, the value of x is 15. To determine the value of y, solve either the first or second given angle measurement and find its supplement.
Solve the first angle using the value of x, which is 15:
(2x + 5)°
- 2x + 5; x = 15
- 2(15) + 5
- 30 + 5
- 35
Find the supplement of 35.
- 180 = x + 35
- 180 - 35 = x
- 145 = x
Therefore, the value of y is 145.
