Math Problem Statement

In the diagram, WY bisects ∠XWZ, and m∠YWZ = 49°. Find m∠XWY and m∠XWZ.

Solution

Let's analyze the problem step by step.

The problem states:

  • WY\overrightarrow{WY} bisects XWZ\angle XWZ.
  • mYWZ=49m \angle YWZ = 49^\circ.

We need to find:

  1. mXWYm \angle XWY
  2. mXWZm \angle XWZ.

Step 1: Use the fact that WYWY bisects XWZ\angle XWZ

Since WYWY bisects XWZ\angle XWZ, it divides XWZ\angle XWZ into two equal parts. This means: mXWY=mYWZ=49m \angle XWY = m \angle YWZ = 49^\circ

So, mXWY=49m \angle XWY = 49^\circ.

Step 2: Calculate mXWZm \angle XWZ

Since WYWY bisects XWZ\angle XWZ and each part is 4949^\circ, the total angle XWZXWZ is twice 4949^\circ: mXWZ=49+49=98m \angle XWZ = 49^\circ + 49^\circ = 98^\circ

Final answers:

  • mXWY=49m \angle XWY = 49^\circ
  • mXWZ=98m \angle XWZ = 98^\circ

Would you like a further explanation or have any other questions?

Here are 5 related questions:

  1. What does it mean for a line to bisect an angle?
  2. How do you determine the total angle from two equal bisected angles?
  3. What is the sum of angles in a triangle?
  4. Can you explain what complementary and supplementary angles are?
  5. How would you solve this problem if only one of the angles was given?

Tip: When dealing with bisected angles, always remember that each half is equal, and you can double one of them to find the full angle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angle Bisectors

Formulas

If a line bisects an angle, the two resulting angles are equal.
Total angle = 2 × bisected angle.

Theorems

Angle Bisector Theorem

Suitable Grade Level

Grades 7-9