Question

consider the diagram. points b and n lie on a straight line.
diagram showing a coordinate-like system with point y, lines, angles: angle between yn and ya is 132°, angle between yg and yi is x°, and by is perpendicular to gy
determine the value of x.
answer
x = blank box

Explanation:

Step1: Find the adjacent angle to 132°

Since points B and N are on a straight line, the angle adjacent to 132° (∠NYA) and the angle ∠NYI are supplementary? Wait, no, actually, ∠AYN is 132°, so the angle ∠NYI (let's call it y) and ∠AYN are supplementary? Wait, no, ∠AYN and ∠NYI: since AYI is a straight line? Wait, no, AYI is a straight line? Wait, the diagram: points A, Y, I are colinear? Wait, the angle at Y between AY and IY: since ∠AYN is 132°, then ∠NYI = 180° - 132° = 48°, because AY and IY are a straight line (so they form a linear pair, sum to 180°). So ∠NYI = 48°.

Step2: Use the right angle

Now, the angle between GY and NY is 90° (since there's a right angle symbol between BY and GY, and BY and NY are a straight line, so GY is perpendicular to BN, so ∠GYN = 90°). Then, ∠GYI is x°, and ∠NYI is 48°, so x + 48° = 90°, because ∠GYN is 90°, which is the sum of x and ∠NYI. So x = 90° - 48° = 42°.

Answer:

42