Math Problem Statement

Solve for m∠XVW given that m∠WVU = 36° and m∠UVW = 76°.

Solution

To solve for mXVWm\angle XVW, we can use the fact that the angles around point VV form a full circle, which sums to 360360^\circ.

We are given:

  • mWVU=36m\angle WVU = 36^\circ
  • mUVW=76m\angle UVW = 76^\circ

Since mXVWm\angle XVW is the remaining part of the full circle, we can calculate it as follows:

mXVW=360(mWVU+mUVW)m\angle XVW = 360^\circ - (m\angle WVU + m\angle UVW)

Substituting the given values:

mXVW=360(36+76)m\angle XVW = 360^\circ - (36^\circ + 76^\circ) mXVW=360112=248m\angle XVW = 360^\circ - 112^\circ = 248^\circ

Thus, mXVW=248m\angle XVW = 248^\circ.

Would you like more details or have any questions? Here are some related questions you might want to explore:

  1. How do angles around a point add up to 360360^\circ?
  2. What is the difference between interior and exterior angles in polygons?
  3. How can you use the sum of angles in a triangle to find missing angles?
  4. What are supplementary and complementary angles, and how do they differ?
  5. How can you apply angle sum properties in different geometrical shapes?

Tip: Always check if the sum of angles around a point adds up to 360360^\circ when dealing with multiple angles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Sum of Angles around a Point

Formulas

Sum of angles around a point: 360°

Theorems

Sum of Angles around a Point Theorem

Suitable Grade Level

Grades 7-9