Answer:
the measures of all angles are 50 degrees, 130 degrees, 180 degrees, and 0 degrees.
Explanation:
Let's label the angles formed by the intersection of two lines as angle A, angle B, angle C, and angle D.
According to the given information, the sum of the measures of two of the angles is 50 degrees. Let's assume angle A and angle B are the angles with the sum of 50 degrees.
So, we have angle A + angle B = 50 degrees.
Since angles A and B are adjacent angles at the intersection of two lines, we know that they form a straight line, which means their sum is 180 degrees.
Therefore, we can write the equation as angle A + angle B = 180 degrees.
From the two equations, we can conclude that angle A + angle B = 50 degrees = 180 degrees.
To find the measures of all angles, we need to solve the equation.
Subtracting angle B from both sides, we get angle A = 180 degrees - angle B.
Now we substitute this value into the first equation:
(180 degrees - angle B) + angle B = 50 degrees.
Simplifying the equation, we get:
180 degrees = 50 degrees + angle B.
Subtracting 50 degrees from both sides, we get:
angle B = 180 degrees - 50 degrees.
Therefore, angle B = 130 degrees.
Now, to find angle A, we substitute the value of angle B into angle A = 180 degrees - angle B:
angle A = 180 degrees - 130 degrees.
Simplifying the equation, we get:
angle A = 50 degrees.
So, the measures of the angles are:
angle A = 50 degrees,
angle B = 130 degrees,
angle C = 180 degrees (since it is a straight line),
angle D = 0 degrees (since it is a straight line).
Therefore, the measures of all angles are 50 degrees, 130 degrees, 180 degrees, and 0 degrees