Two lines intersect to form two pairs of vertical angles.Angle 1 with measure (20x + 7) degrees and angle 3 with measure (5x + 7y + 49) degrees are vertical angles. Angle 2 with measure (3x - 2y + 30) degrees and angle 4 are vertical angles.Find the values x and y and the measure of all four angles.
To find the values of x and y, and the measure of all four angles, we can use the property of vertical angles. Vertical angles are formed when two lines intersect and are opposite to each other. These angles have equal measures.
Given:
Angle 1 = 20x + 7
Angle 3 = 5x + 7y + 49
Angle 2 = 3x - 2y + 30
Angle 4 (measure not specified)
Since angles 1 and 3 are vertical angles, their measures are equal:
20x + 7 = 5x + 7y + 49
Similarly, angles 2 and 4 are vertical angles, so their measures are equal:
3x - 2y + 30 = Angle 4
Now we have two equations with two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
Equation 1: 20x + 7 = 5x + 7y + 49
Subtract 5x and 7 from both sides:
15x - 5x = 7y - 7 + 49
10x = 7y + 42
Equation 2: 3x - 2y + 30 = Angle 4
Now we need more information to find the values of x and y, and the measure of angle 4.