Two angles whose sum is 180° are called supplementary angles. The value of x and y is 65° and 70°, respectively.
What are supplementary angles?
Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
For the given figure, the pair of ∠A and ∠C are vertically opposite angles. therefore, the measure of the two angles will be equal. Thus, we can write,
∠A = ∠C
x + 45 = 3x - 85
x - 3x = -85 - 45
-2x = -130°
x = -130/-2
x = 65°
Hence, the value of x is 65°.
Also, in the given figure the pair of ∠A and ∠B will form a linear pair, or can be said will be supplementary to each other, therefore, we can write the sum of the two angles as,
∠A + ∠B = 180°
x + 45° + y = 180°
Substitute the value of x,
65° + 45° + y = 180
y = 180° - 65° - 45°
y = 70°
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