The exterior angle PRS of triangle PQR is $105^o$. If $\angle Q=70^o$, find $\angle P$. Is $\angle PRS > \angle P$.

Given:

The exterior angle PRS of triangle PQR is $105^o$.

$\angle Q=70^o$.
To do:

We have to find $\angle P$.

Solution:

We know that,

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.
Therefore,

$\angle PRS=\angle PQR+\angle RPQ$

$105^o=70^o+\angle RPQ$

$\angle RPQ=105^o-70^o$

$\angle RPQ=35^o$
As we can see, $\angle PRS > \angle P$.

The measure of $ \angle P$ is $35^o$.

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Updated on: 10-Oct-2022

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