Question

Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale.

A. 52°
B. 26°
C. 104°
D. 38°​

Answer 1

x = 52°

Option (a)

Explanation:

Check attachment for diagram for this illustration.

From the diagram in the attachment.

Since line PN = line NQ and PM = OM, angle PMN will also be equal = Angle POQ = 90° right angle.

PMN = POQ = 90°

From this we can find angle NPM

Angle NPM = 180 - (angle M + angle N) ... angle in a triangle

Angle NPM = 180 - (90 + 52)

NPM = 180 - 142 = 38°

Haven gotten angle P = 38°, We can now find our angle x (Q) in triangle OPQ

Angle Q = 180 - ( angle O + angle P) ... angle in a triangle

Angle Q = 180 - ( 90 + 38)

Angle Q = 180 - 138 = 52°

Therefore x = 52°

Answer 2

C.
`104°`

Explanation:

This is what is called the Mid-segment Theorem, which states that the relation of a triangle's midpunkt is parallel to the triangle's third side, and the mid-segment length is half the third side length, so you would double 52° to get 104°.

I am joyous to assist you anytime.