For the triangle to be acute, all three angles must measure less than $\displaystyle 90 ^{\circ }$. We can eliminate $\displaystyle 32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $\displaystyle 45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason. 

In an isosceles triangle, at least two angles are congruent, so we can eliminate $\displaystyle 50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$.

The degree measures of the three angles of a triangle must total 180, so, since $\displaystyle 80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$, we can eliminate $\displaystyle 80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$.

$\displaystyle 36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

The degree measures of a triangle total $\displaystyle 180^{\circ }$, so

$\displaystyle x + (x+24) + 2x = 180$

$\displaystyle 4x+24 = 180$

$\displaystyle 4x+24 -24 = 180 -24$

$\displaystyle 4x = 156$

$\displaystyle 4x \div 4 = 156 \div 4$

$\displaystyle x = 39$

The degree measures of the interior angles of a triangle total $\displaystyle 180 ^{\circ }$, so, if we let $\displaystyle x^{\circ }$ be the measure of the unmarked angle, then

$\displaystyle x + 41 + 72 = 180$

$\displaystyle x + 113 = 180$

$\displaystyle x = 67$

Three angles with measures $\displaystyle 67^{\circ}, y^{\circ}, y^{\circ}$ together form a straight angle, so

$\displaystyle y+ y + 67= 180$

$\displaystyle 2y+ 67= 180$

$\displaystyle 2y+ 67- 67 = 180 - 67$

$\displaystyle 2y = 113$

$\displaystyle 2y \div 2 = 113 \div 2$

$\displaystyle y = 56 \frac{1}{2}$

One of the angles of $\displaystyle \Delta EFC$ - namely, $\displaystyle \angle EFC$ - can be seen to be an obtuse angle, as it is wider than a right angle. This makes $\displaystyle \Delta EFC$, by definition, an obtuse triangle.

One of the angles of $\displaystyle \Delta CED$ - namely, $\displaystyle \angle CDE$ - is marked as a right angle. This makes $\displaystyle \Delta CED$, by definition, a right triangle.

A congruency statement about two triangles implies nothing about the relationship between two angles of one of the triangles, so $\displaystyle \angle M \cong \angle N$ is not correct.

Also, letters in the same position between the two triangles refer to corresponding - and subsequently, congruent - angles. Therefore, $\displaystyle \Delta MNO \cong \Delta PQR$ implies that:

$\displaystyle \angle M \cong \angle P$

$\displaystyle \angle N \cong \angle Q$

$\displaystyle \angle O \cong \angle R$

Of the given choices, only $\displaystyle \angle M \cong \angle P$ is a consequence. It is the correct response.

The triangle has an exterior angle of $\displaystyle 130 ^{\circ }$, so it has an interior angle of $\displaystyle (180-130)^{\circ } = 50^{\circ }$. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:

Case 1: Two angles have measure $\displaystyle 50^{\circ }$. The third angle will have measure

$\displaystyle \left [180 - (50 + 50 ) \right ] ^{\circ } = 80 ^{\circ }$.

$\displaystyle 80 ^{\circ }$ will be the greatest of the angle measures.

Case 2: One angle has measure $\displaystyle 50^{\circ }$ and the others are congruent. Their common measure will be

$\displaystyle \frac{1}{2} (180^{\circ }- 50^{\circ } ) = 65 ^{\circ }$.

$\displaystyle 65 ^{\circ }$ will be the greatest of the angle measures.

The given information is therefore inconclusive.

The triangle has an exterior angle of $\displaystyle 130 ^{\circ }$, so it has an interior angle of $\displaystyle (180-130)^{\circ } = 50^{\circ }$. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:

Case 1: Two angles have measure $\displaystyle 50^{\circ }$. The third angle will have measure

$\displaystyle \left [180 - (50 + 50 ) \right ] ^{\circ } = 80 ^{\circ }$.

$\displaystyle 50^{\circ }$ will be the least of the angle measures.

Case 2: One angle has measure $\displaystyle 50^{\circ }$ and the others are congruent. Their common measure will be

$\displaystyle \frac{1}{2} (180^{\circ }- 50^{\circ } ) = 65 ^{\circ }$.

$\displaystyle 50^{\circ }$ will be the least of the angle measures.

In both cases, the least of the degree measures of the angles will be $\displaystyle 50^{\circ }$.

The triangle has an exterior angle of $\displaystyle 70 ^{\circ }$, so it has an interior angle of $\displaystyle (180-70)^{\circ } = 110 ^{\circ }$.

Since this is an obtuse angle, its other two angles must be acute. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles - the acute angles are those. Since the sum of their measures is the same as their remote exterior angle - $\displaystyle 70 ^{\circ }$ - each has measure $\displaystyle 35 ^{\circ }$.This is the correct response.

The triangle has an exterior angle of $\displaystyle 80 ^{\circ }$, so it has an interior angle of $\displaystyle (180-80)^{\circ } = 100 ^{\circ }$.

Since this is an obtuse angle, its other two angles must be acute. Therefore, this angle is the one of greatest measure.