Question

Find X FIND Y PlEase Help me

Answer 1

The X and Y angles created by lines intersection in the pictures are 18° and 54°.

Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:

∠MON = ∠MOA +∠AON = 90°

∠MON = 72° + ∠AON = 90°

∠AON = 18° ... (i)

If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:

∠AOD = ∠BOC

∠AOC = ∠BOD

∠AOD + AOC = 180°

∠BOC + ∠BOD = 180°

Based on the picture, we know that:

∠BOC = x

∠AOC = ∠MOA + ∠MOC

∠AOC = 72° + y ...(ii)

∠AOD = ∠AON + ∠NOD

∠AOD = 18° +2x

∠BOC = 3x ... (iii)

Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:

∠BOC = ∠AOD

3x = 18° + 2x

x = 18° ... (iv)

To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we  know that:

∠AOC + ∠BOC = 180° ... (v)

Input equations (ii) and (iv) into (v)

∠AOC + ∠BOC = 180°

(72° + y) + 3x = 180°

72° + y + 3(18°) = 180°

126° + y = 180°

y = 54° ... (vi)

Learn more about the angles by lines intersection here: brainly.com/question/2077876?referrer=searchResults

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