Given △PQR∼△LMN , m∠Q=113° , and m∠R=26° , what is the measure of angle N ?(1 point) m∠N = °

Answer 1

Since triangles $\mathrm{△}PQR$ and $\mathrm{△}LMN$ are similar (denoted by $\mathrm{△}PQR\sim \mathrm{△}LMN$), the corresponding angles are equal.

In triangle $PQR$:

• $m\mathrm{\angle }Q={113}^{\circ }$
• $m\mathrm{\angle }R={26}^{\circ }$

To find the measure of angle $P$, we can use the fact that the sum of the angles in a triangle is ${180}^{\circ }$:

$$m\mathrm{\angle }P+m\mathrm{\angle }Q+m\mathrm{\angle }R={180}^{\circ }$$ $$m\mathrm{\angle }P+{113}^{\circ }+{26}^{\circ }={180}^{\circ }$$ $$m\mathrm{\angle }P+{139}^{\circ }={180}^{\circ }$$ $$m\mathrm{\angle }P={180}^{\circ }-{139}^{\circ }={41}^{\circ }$$

Now, in triangle $LMN$, the corresponding angles must match:

• $m\mathrm{\angle }L=m\mathrm{\angle }P={41}^{\circ }$
• $m\mathrm{\angle }M=m\mathrm{\angle }Q={113}^{\circ }$
• $m\mathrm{\angle }N=m\mathrm{\angle }R={26}^{\circ }$

Therefore, the measure of angle $N$ is:

$$m\mathrm{\angle }N={26}^{\circ }$$

So, $m\mathrm{\angle }N={26}^{\circ }$.