Question

12. In APOR, PQ = QR. If m2P = (3x – 120) and MZR = (x-30)", classify APQR. Select all that

apply.
A acute
right
B obtuse
O equilateral
scalene
isosceles

Answer 1

Isosceles (E) & obtuse (B)

Explanation:

Since PQ = QR, △PQR = isosceles triangle (opposite sides are equal).

If, PQ = QR, then, m∠Q = ∠R (measure of opposite angles are same if opposite sides are equal in a triangle).

Then, using Angle sum property,

m∠P + m∠Q + m∠R = 180°

3x - 120 + x - 30 + x - 30 = 180

3x + x + x - 120 - 30 - 30 = 180

5x - 180 = 180, 5x = 180 + 180

5x = 360

x = 72.

So, (3x - 120)° = 96°

(x - 30)° = 42

So, △PQR = obtuse (one angle is < 90°)

=》 Then, △PQR = isosceles (E) & obtuse (B) .

Hope it helps ⚜