Question

In ΔPQR, ∠P = 80° and ∠Q = 43°. Arrange the sides in descending order of length.

Answer 1

Given:

Triangle ΔPQR with ∠P = 80°, ∠Q = 43°

Step 1: Find the third angle

∠R = 180° – (80° + 43°) = 180° – 123° = 57°

So, the angles are ∠P = 80°, ∠Q = 43°, ∠R = 57°

Step 2: Relating sides to angles

In any triangle, the largest angle is opposite the longest side and the smallest angle is opposite the shortest side.

Largest angle = ∠P = 80° → Opposite side = QR  ...(Longest side) 

Next = ∠R = 57° → Opposite side = PQ   ...(Middle side)

Smallest angle = ∠Q = 43° → Opposite side = PR   ...(Shortest side)

The sides in descending order of length are QR > PQ > PR.