We need to find the size of angle $p$. The figure shows two lines intersecting at a point. The angles on one side of the intersection are $12^{\circ}$, $21^{\circ}$, and $14^{\circ}$. The angle on the other side of the intersection is $p$.

GeometryAnglesIntersecting LinesAngle Sum
2025/5/5

1. Problem Description

We need to find the size of angle pp. The figure shows two lines intersecting at a point. The angles on one side of the intersection are 1212^{\circ}, 2121^{\circ}, and 1414^{\circ}. The angle on the other side of the intersection is pp.

2. Solution Steps

Since the lines intersect, the sum of angles on one side of the intersection point must be equal to the sum of angles on the other side. The sum of the angles on one side is 12+21+1412^{\circ} + 21^{\circ} + 14^{\circ}.
12+21+14=4712 + 21 + 14 = 47
So, the sum is 4747^{\circ}.
Since the angles are equal, p=47p = 47^{\circ}.

3. Final Answer

p=47p = 47^{\circ}

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