The lengths of sides XY, YZ, and XZ of triangle XYZ are 7 cm, 12 cm, and 15 cm respectively.

The lengths of sides XY, YZ, and XZ of triangle XYZ are 7 cm, 12 cm, and 15 cm respectively. What angle of the triangle has the largest measure? A. Angle X B. Angle Z C. Angle Y D. Cannot be determined What is the shortest side of triangle PQR if m(P) = 65 and m(LQ) = 58? A. PQ B. PR C. QR D. RP

The Correct Answer and Explanation is:

Correct Answers:

1. Angle with the largest measure in triangle XYZ: C. Angle Y
2. Shortest side of triangle PQR: C. QR

Explanation:

Question 1: Triangle XYZ

You are given the lengths of all three sides:

• XY = 7 cm
• YZ = 12 cm
• XZ = 15 cm

In any triangle, the angle opposite the longest side is the largest angle.
Here, the longest side is XZ = 15 cm, so the angle opposite XZ is Angle Y.

Therefore, the largest angle is Angle Y, and the correct answer is:
C. Angle Y

Question 2: Triangle PQR

You are given the measures of two angles:

• m∠P = 65°
• m∠Q = 58°

To find the third angle, use the triangle angle sum property:
Sum of angles in any triangle = 180°
So,
m∠R = 180° − (65° + 58°) = 57°

Now compare the angle measures:

• m∠P = 65°
• m∠Q = 58°
• m∠R = 57°

In any triangle, the shortest side is opposite the smallest angle.
The smallest angle here is Angle R = 57°, so the shortest side is opposite to Angle R, which is side PQ.

But wait — that seems off.
Angle R = 57° → side opposite is PQ
Angle Q = 58° → side opposite is PR
Angle P = 65° → side opposite is QR

Since Angle R = 57° is the smallest, side PQ is opposite it.
So PQ is the shortest side.

Corrected answer: A. PQ

So the correct answers are:

1. C. Angle Y
2. A. PQ

Apologies for the earlier mistake in the second question — the correct shortest side is PQ, not QR.