The problem asks to find the value of $p$ in the given triangle where the exterior angles are $3p$, $3p$, and $6p$.

GeometryTrianglesExterior AnglesAngle SumAlgebraic Manipulation
2025/7/16

1. Problem Description

The problem asks to find the value of pp in the given triangle where the exterior angles are 3p3p, 3p3p, and 6p6p.

2. Solution Steps

The sum of the exterior angles of any polygon is 360360 degrees. In this case, the polygon is a triangle. Thus, the sum of the exterior angles of the given triangle is 3p+3p+6p=3603p + 3p + 6p = 360.
Simplifying the left side, we have 12p=36012p = 360.
Dividing both sides by 1212, we get
p=36012=30p = \frac{360}{12} = 30.

3. Final Answer

p=30p = 30

Related problems in "Geometry"

We are given that $\overline{EJ} \parallel \overline{FK}$, $\overline{JG} \parallel \overline{KH}$, ...

GeometryTriangle CongruenceParallel LinesASA Congruence PostulateProofs
2025/7/16

We are asked to find the value of $y$ in the figure. The polygon has angles $4y$, $4y$, $5y$, $2y$, ...

PolygonInterior AnglesAngle Sum Formula
2025/7/16

The image shows a circle divided into sectors. We are given the degree measures of three sectors: $7...

CircleAnglesSectorCentral Angle
2025/7/16

We have a quadrilateral $ABCD$. Angle $B$ and angle $D$ are right angles. $AB = 10M$. Angle $BAC$ is...

QuadrilateralsTrianglesRight TrianglesIsosceles TrianglesTrigonometryPythagorean TheoremAngle Properties
2025/7/16

We are given a diagram with two lines and angles labeled $x$, $y$, and $z$. The line segment $PQ$ is...

Parallel LinesAnglesTriangle Angle Sum TheoremGeometric Proof
2025/7/16

The problem provides a diagram with lines and angles marked as $x$, $y$, and $z$. The line $PQ$ is p...

Parallel LinesAnglesTransversalsTriangle Angle SumGeometric Proof
2025/7/16

Determine the relationship between angles $x$ and $y$ in the given diagram, where the lines $PQ$ and...

Parallel LinesAnglesAlternate Interior AnglesStraight LinesGeometric Proof
2025/7/16

We are given a diagram with parallel lines and a triangle. We are asked to find the relationship bet...

Parallel LinesTrianglesAngle RelationshipsEuclidean Geometry
2025/7/16

We are given a diagram with two lines that appear parallel (based on the arrowhead on line $PQ$ and ...

Parallel LinesTransversalsAnglesTriangle Angle Sum TheoremExterior Angles
2025/7/16

The image shows two parallel lines, $PQ$ and $RS$, intersected by a transversal line. There is also ...

Parallel LinesTransversalTrianglesAngle RelationshipsAlternate Interior AnglesCorresponding AnglesAngle Sum Property
2025/7/16