The problem asks to find the value of $x$ given that a circle is divided into three angles: $189^\circ$, $148^\circ$, and $x^\circ$.

GeometryAnglesCirclesEquation Solving
2025/4/28

1. Problem Description

The problem asks to find the value of xx given that a circle is divided into three angles: 189189^\circ, 148148^\circ, and xx^\circ.

2. Solution Steps

The sum of the angles in a full circle is 360360^\circ. Therefore, the sum of the three given angles must be equal to 360360^\circ.
189+148+x=360189^\circ + 148^\circ + x^\circ = 360^\circ
First, we add 189189 and 148148:
189+148=337189 + 148 = 337
So, we have:
337+x=360337 + x = 360
Now, we subtract 337337 from both sides of the equation to solve for xx:
x=360337x = 360 - 337
x=23x = 23

3. Final Answer

The value of xx is 23.

Related problems in "Geometry"

The problem consists of two parts: (a) A window is in the shape of a semi-circle with radius 70 cm. ...

CircleSemi-circlePerimeterBase ConversionNumber Systems
2025/6/11

The problem asks us to find the volume of a cylindrical litter bin in m³ to 2 decimal places (part a...

VolumeCylinderUnits ConversionProblem Solving
2025/6/10

We are given a triangle $ABC$ with $AB = 6$, $AC = 3$, and $\angle BAC = 120^\circ$. $AD$ is an angl...

TriangleAngle BisectorTrigonometryArea CalculationInradius
2025/6/10

The problem asks to find the values for I, JK, L, M, N, O, PQ, R, S, T, U, V, and W, based on the gi...

Triangle AreaInradiusGeometric Proofs
2025/6/10

In triangle $ABC$, $AB = 6$, $AC = 3$, and $\angle BAC = 120^{\circ}$. $D$ is the intersection of th...

TriangleLaw of CosinesAngle Bisector TheoremExternal Angle Bisector TheoremLength of SidesRatio
2025/6/10

A hunter on top of a tree sees an antelope at an angle of depression of $30^{\circ}$. The height of ...

TrigonometryRight TrianglesAngle of DepressionPythagorean Theorem
2025/6/10

A straight line passes through the points $(3, -2)$ and $(4, 5)$ and intersects the y-axis at $-23$....

Linear EquationsSlopeY-interceptCoordinate Geometry
2025/6/10

The problem states that the size of each interior angle of a regular polygon is $135^\circ$. We need...

PolygonsRegular PolygonsInterior AnglesExterior AnglesRotational Symmetry
2025/6/9

Y is 60 km away from X on a bearing of $135^{\circ}$. Z is 80 km away from X on a bearing of $225^{\...

TrigonometryBearingsCosine RuleRight Triangles
2025/6/8

The cross-section of a railway tunnel is shown. The length of the base $AB$ is 100 m, and the radius...

PerimeterArc LengthCircleRadius
2025/6/8