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Calculate the missing angles a, b, c, and d in the diagram below, giving a reason for each answer

Calculate the missing angles a, b, c, and d in the diagram below, giving a reason-example-1
User Espeed
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Answer:

see below and attachment

Explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a. Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b. Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c. These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°. We have 30°, 50°, so the last angle must be 100°. We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°. We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps! See attachment for visual.

Calculate the missing angles a, b, c, and d in the diagram below, giving a reason-example-1
User PikkuKatja
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