Math

QuestionXYundefined\overrightarrow{X Y} bisects WXZ\angle W X Z with mZXY=37m \angle Z X Y=37^{\circ}. Find mWXYm \angle W X Y and mZXWm \angle Z X W.

Studdy Solution

STEP 1

Assumptions1. XYundefined\overrightarrow{XY} bisects WXZ\angle WXZ . mZXY=37m \angle ZXY =37^{\circ}

STEP 2

Since XYundefined\overrightarrow{XY} bisects WXZ\angle WXZ, it means that WXZ\angle WXZ is divided into two equal angles. Therefore, mZXY=mWXYm \angle ZXY = m \angle WXY.

STEP 3

Substitute the given value of mZXYm \angle ZXY to find mWXYm \angle WXY.
mWXY=mZXY=37m \angle WXY = m \angle ZXY =37^{\circ}

STEP 4

To find mZXWm \angle ZXW, we need to understand that the sum of the angles in a triangle is 180180^{\circ}. Therefore, mZXW=180mZXYmWXYm \angle ZXW =180^{\circ} - m \angle ZXY - m \angle WXY.

STEP 5

Substitute the values of mZXYm \angle ZXY and mWXYm \angle WXY into the equation to find mZXWm \angle ZXW.
mZXW=1803737m \angle ZXW =180^{\circ} -37^{\circ} -37^{\circ}

STEP 6

Calculate the value of mZXWm \angle ZXW.
mZXW=1803737=106m \angle ZXW =180^{\circ} -37^{\circ} -37^{\circ} =106^{\circ}So, mWXY=37m \angle WXY =37^{\circ} and mZXW=106m \angle ZXW =106^{\circ}.

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