Question
In $\triangle\text{LMN},\angle\text{L}=50^\circ$ and $\angle\text{L}=60^\circ.$ If $\triangle\text{LMN}\sim\triangle\text{PQR},$ then find $\angle\text{Q}.$
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Answer
$\angle\text{L}+\angle\text{M}+\angle\text{N}=180^\circ$ (Angle sum property)Substituting $\angle\text{L}=50^\circ$ and $\angle\text{N}=60^\circ$ in this equation:
$50^\circ+\angle\text{M}+60^\circ=180^\circ$
$\angle\text{M}=70^\circ$
It is given that $\triangle\text{LMN}\sim\triangle\text{PQR}.$
We know that corresponding angle in similar triangles are of equal measures.
$\therefore\ \angle\text{M}=\angle\text{Q}=70^\circ$
Thus, the measure of $\angle\text{Q}$ is 70º
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