In a triangle PQR if ∠QPR = 80° and PQ = PR, then ∠R and ∠Q are

In a triangle PQR, if ∠QPR = 80° and PQ = PR, this means that the triangle is an isosceles triangle (two sides are equal).

In an isosceles triangle, the angles opposite the equal sides are equal. So, ∠R = ∠Q.

We also know that the sum of all angles in a triangle is 180°.

So, ∠P + ∠Q + ∠R = 180°

We know that ∠P = 80°, so we can substitute this into the equation:

80° + ∠Q + ∠R = 180°

Since ∠Q = ∠R, we can simplify this to:

80° + 2∠Q = 180°

Subtract 80° from both sides to isolate the term with ∠Q:

2∠Q = 100°

Finally, divide both sides by 2 to solve for ∠Q:

∠Q = 50°

And since ∠Q = ∠R, ∠R is also 50°.

So, ∠R and ∠Q are both 50°.