Question

"For triangle △PQR, if ∡P = 70° and ∡Q = 35°, which side of the triangle is the longest side?

A) The longest side is QR because ∠P is the largest angle with ∡R = 65°.
B) The longest side is PQ because ∠R is the largest angle with ∡R = 75°.
C) It is impossible to determine without being given ∡R.
D) The longest side is PR because ∠Q has the smallest angle measure.

Please select the correct statement."

Answer 1

The longest side of triangle △PQR is side PQ because it is opposite the largest angle, which is ∠R with a measure of 75°.

Step-by-step explanation:

To determine which side of triangle △PQR is the longest, we can use the property that in any triangle, the side opposite the largest angle is the longest side. Given ∠P = 70° and ∠Q = 35°, we can find ∠R by subtracting the sum of ∠P and ∠Q from 180°, the total sum of angles in a triangle.

∠R = 180° - (∠P + ∠Q) = 180° - (70° + 35°) = 180° - 105° = 75°.

Since ∠R is the largest angle (∠R = 75°), the longest side is opposite ∠R, which is side PQ. Therefore, the correct statement is:

B) The longest side is PQ because ∠R is the largest angle with ∠R = 75°.