We are given two intersecting lines. One angle is labeled as $123^\circ$ and the angle adjacent to it is labeled as $(2v+1)^\circ$. We need to find the value of $v$.

GeometryAnglesLinear EquationsSupplementary AnglesAlgebra
2025/3/27

1. Problem Description

We are given two intersecting lines. One angle is labeled as 123123^\circ and the angle adjacent to it is labeled as (2v+1)(2v+1)^\circ. We need to find the value of vv.

2. Solution Steps

Since the two angles are adjacent and form a straight line, they are supplementary angles. This means their sum is 180180^\circ.
Therefore, we can write the equation:
123+(2v+1)=180123 + (2v+1) = 180
Now we solve for vv.
123+2v+1=180123 + 2v + 1 = 180
124+2v=180124 + 2v = 180
2v=1801242v = 180 - 124
2v=562v = 56
v=562v = \frac{56}{2}
v=28v = 28

3. Final Answer

The value of vv is
2
8.

Related problems in "Geometry"

The problem asks to find the volume of a pentagonal pyramid. The base is a regular pentagon with sid...

VolumePyramidPentagonArea Calculation3D Geometry
2025/5/8

A rectangle $PQRS$ with length $20$ cm and width $10+10 = 20$ cm has a square of side $x$ cm cut out...

AreaRectangleSquareGeometric Shapes
2025/5/8

We are given the coordinates of the vertices of a quadrilateral MATH: $M(-1, 7)$, $A(3, 5)$, $T(2, -...

Coordinate GeometryQuadrilateralsTrapezoidsSlopeParallel Lines
2025/5/8

The problem describes a rectangle $PQRS$ from which a square of side $x$ cm has been cut. The dimens...

AreaRectangleSquareGeometric ShapesAlgebraic Equations
2025/5/8

The problem asks to find the radius of a circle given a central angle of $\frac{4\pi}{3}$ radians an...

CircleArc LengthRadianGeometry
2025/5/7

The problem seems to involve finding the area of triangle $ABC$. The given information appears to be...

Area of a TriangleTrigonometryGeometric Formulas
2025/5/7

The problem asks for the equation of a circle centered at the origin $(0, 0)$ that passes through th...

Circle EquationCoordinate GeometryRadiusOrigin
2025/5/7

The problem asks to find the equation of a circle given its graph. We can identify two points on the...

CirclesEquation of a CircleCoordinate GeometryDistance Formula
2025/5/7

The problem asks us to write the equation of a circle with center $(-4, -6)$ and diameter 8. The giv...

Circle EquationGeometryCoordinate GeometryRadius and Diameter
2025/5/7

The problem asks to find the equation of a circle with center $(-2, 5)$ and radius $8$.

Circle EquationCoordinate Geometry
2025/5/7