31. One of the angle measures of a right triangle is $$ 36^{\circ} $$. Which of the following is the measure of one of the other two angles of the triangle? $$ \begin{array}{ll} ext { A. } 36^{\circ} & ext { B. } 44^{\circ} \ ext { C. } 54^{\circ} & ext { D. } 144^{\circ}\end{array} $$ 32. Two of the angles of a triangle measure $$ 42^{\circ} $$ and $$ 67^{\circ} $$. The side opposite which angle of the triangle is the longest side? Explain your

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31. One of the angle measures of a right triangle is $$ 36^{\circ} $$. Which of the following is the measure of one of the other two angles of the triangle? $$ \begin{array}{ll}	ext { A. } 36^{\circ} & 	ext { B. } 44^{\circ} \ 	ext { C. } 54^{\circ} & 	ext { D. } 144^{\circ}\end{array} $$ 32. Two of the angles of a triangle measure $$ 42^{\circ} $$ and $$ 67^{\circ} $$. The side opposite which angle of the triangle is the longest side? Explain your

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**31.**

A right triangle has one angle of $$90^{\circ}$$, and one of the given angles is $$36^{\circ}$$. The sum of the angles in any triangle is $$180^{\circ}$$. Let the third angle be $$x$$; then

$$
90^{\circ} + 36^{\circ} + x = 180^{\circ}.
$$

Subtracting $$90^{\circ} + 36^{\circ}$$ from both sides, we have

$$
x = 180^{\circ} - 90^{\circ} - 36^{\circ} = 54^{\circ}.
$$

Thus, one of the other angles is $$54^{\circ}$$.  
Answer: Option C.

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**32.**

A triangle has angles measuring $$42^{\circ}$$, $$67^{\circ}$$, and let the third angle be $$x$$. Using the angle sum property:

$$
42^{\circ} + 67^{\circ} + x = 180^{\circ}.
$$

Calculating $$x$$:

$$
x = 180^{\circ} - 42^{\circ} - 67^{\circ} = 71^{\circ}.
$$

The triangle's angles are $$42^{\circ}$$, $$67^{\circ}$$, and $$71^{\circ}$$. In any triangle, the longest side is opposite the largest angle. Here, the largest angle is $$71^{\circ}$$. Therefore, the side opposite the angle measuring $$71^{\circ}$$ is the longest side.
**31.** One of the other angles is $$54^{\circ}$$. **32.** The side opposite the $$71^{\circ}$$ angle is the longest side because it's the largest angle in the triangle.

One of the angle measures of a right triangle is
. Which of the following is the measure of
one of the other two angles of the triangle?

Two of the angles of a triangle measure and
. The side opposite which angle of the
triangle is the longest side? Explain your

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One of the angle measures of a right triangle is . Which of the following is the measure of one of the other two angles of the triangle? Two of the angles of a triangle measure and . The side opposite which angle of the triangle is the longest side? Explain your