Question

congruent triangles quiz. which of the following is the correct classification of $\triangle mnp$ if $mangle m = 35^{circ}$ and $mangle p = 47^{circ}$? equiangular, obtuse, right, acute

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle M = 35^{\circ}$ and $\angle P=47^{\circ}$, and $\angle N$ be the third - angle. Then $m\angle M + m\angle N + m\angle P=180^{\circ}$.

Step2: Calculate the measure of $\angle N$

We can find $m\angle N$ by substituting the known values into the angle - sum formula: $m\angle N=180^{\circ}-m\angle M - m\angle P$. Substituting $m\angle M = 35^{\circ}$ and $m\angle P = 47^{\circ}$, we get $m\angle N=180^{\circ}-35^{\circ}-47^{\circ}=98^{\circ}$.

Step3: Classify the triangle based on angle measures

An equiangular triangle has all angles equal to $60^{\circ}$. An obtuse triangle has one angle greater than $90^{\circ}$. A right triangle has one angle equal to $90^{\circ}$. An acute triangle has all angles less than $90^{\circ}$. Since $m\angle N = 98^{\circ}>90^{\circ}$, $\triangle MNP$ is an obtuse triangle.

Answer:

B. Obtuse