The bunting flags are all isosceles triangles. We are given an isosceles triangle $PQR$ with angle $QPR = 76^{\circ}$. We need to find the size of angle $PRQ$.

GeometryTrianglesIsosceles TriangleAngle CalculationGeometry
2025/6/8

1. Problem Description

The bunting flags are all isosceles triangles. We are given an isosceles triangle PQRPQR with angle QPR=76QPR = 76^{\circ}. We need to find the size of angle PRQPRQ.

2. Solution Steps

Since triangle PQRPQR is an isosceles triangle with PR=QRPR = QR, the angles opposite these sides are equal, i.e., anglePQR=angleQPRangle PQR = angle QPR. Therefore, anglePQR=76angle PQR = 76^{\circ}.
The sum of the angles in a triangle is 180180^{\circ}.
Therefore, we have
anglePQR+angleQPR+anglePRQ=180angle PQR + angle QPR + angle PRQ = 180^{\circ}.
Substituting the known values, we have
76+76+anglePRQ=18076^{\circ} + 76^{\circ} + angle PRQ = 180^{\circ}.
152+anglePRQ=180152^{\circ} + angle PRQ = 180^{\circ}.
anglePRQ=180152angle PRQ = 180^{\circ} - 152^{\circ}.
anglePRQ=28angle PRQ = 28^{\circ}.

3. Final Answer

The size of angle PRQPRQ is 2828^{\circ}.

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