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Question
In the given figure, ∠P = 40°, ∠Q= 90°, and PQ = 12 m. PX and QX are the respective angle bisectors of P and Q. If PX and QX are bisected perpendicularly by AY and BZ, respectively, then ∠YXZ is:
In the given figure, ∠P = 40°, ∠Q= 90°, and PQ = 12 m. PX and QX are the respective angle bisectors of P and Q. If PX and QX are bisected perpendicularly by AY and BZ, respectively, then ∠YXZ is:
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Solution
The correct option is B 50∘
Every point on the perpendicular bisector is equidistant from the segment's endpoints.
XY = PY [Perpendicular bisector theorem]
∠YXP=20∘ [Angles opposite to equal sides are equal]
In △PXQ,
∠PXQ=180∘−∠ZQX−∠YPX [Angle sum property]
∠PXQ=180∘−45∘−20∘=115∘
∠YXZ=∠PXQ−∠ZXQ−∠YXP
∠YXZ=115∘−45∘−20∘=50∘.
Every point on the perpendicular bisector is equidistant from the segment's endpoints.
XY = PY [Perpendicular bisector theorem]
∠YXP=20∘ [Angles opposite to equal sides are equal]
In △PXQ,
∠PXQ=180∘−∠ZQX−∠YPX [Angle sum property]
∠PXQ=180∘−45∘−20∘=115∘
∠YXZ=∠PXQ−∠ZXQ−∠YXP
∠YXZ=115∘−45∘−20∘=50∘.
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