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Q10.
Expert-verifiedWrite proofs in two-column form.
Given: $\overline{VY}\perp \overline{YZ}$. Prove: $\angle VXZ$ is an obtuse angle.
Statement | Reason |
1. $\angle Y+\angle Z+\angle YXZ=180$ | Angle sum property |
2. $\angle YXZ+\angle VXZ=180$ | Linear angles |
The sum of the angles of a triangle is 180. If an angle is greater than 90 then it is an obtuse angle.
Since $\overline{VY}\perp \overline{YZ}$ therefore, $\angle XYZ=\angle Y=90$.
The sum of the angles of triangle will be:
role="math" localid="1637852883028" $\begin{array}{c}\angle Y+\angle Z+\angle YXZ=180\\ \angle Z+\angle YXZ=180-\angle Y\\ \angle Z+\angle YXZ=180-90\\ \angle Z+\angle YXZ=90\end{array}$
Since $\angle Z>90$, therefore $\angle YXZ<90$.
From the figure
Use linear angle property as follows:
$\angle YXZ+\angle VXZ=180$
Since $\angle YXZ<90$ therefore from equation (1) $\angle VXZ>90$.
Therefore, $\angle VXZ$ is an obtuse angle.
Hence proved.
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