Question

If ∆ABC ~∆ PQR and angle P = 50° ,angle B =60 °. Find angle R,

Answer 1

To find angle R in similar triangles ∆ABC and ∆PQR, given angle P is 50° and angle B (which is equivalent to angle Q) is 60°, subtract the sum of angles P and Q from 180° to get angle R = 70°.

Step-by-step explanation:

If ∆ABC ≅ ∆PQR and angle P = 50° and angle B = 60°, to find angle R, we use the fact that corresponding angles in similar triangles are equal.

In similar triangles ∆ABC and ∆PQR:

• Angle A corresponds to Angle P,
• Angle B corresponds to Angle Q, and
• Angle C corresponds to Angle R.

Given that angle B is 60°, this must equal angle Q because they are corresponding angles and the triangles are similar.

Since the sum of angles in a triangle is always 180°, we can find angle R by subtracting the known angles from 180°:
180° - angle P - angle Q = angle R.

Therefore, angle R = 180° - 50° - 60° = 70°.