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:
- bisects .
- .
We need to find:
- .
Step 1: Use the fact that bisects
Since bisects , it divides into two equal parts. This means:
So, .
Step 2: Calculate
Since bisects and each part is , the total angle is twice :
Final answers:
Would you like a further explanation or have any other questions?
Here are 5 related questions:
- What does it mean for a line to bisect an angle?
- How do you determine the total angle from two equal bisected angles?
- What is the sum of angles in a triangle?
- Can you explain what complementary and supplementary angles are?
- 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