Question #6435347Single Choice
Geometry
Question

Find the value of m and n.
Options
A
30, 60
B
60, 30
C
60, 45
D
90, 60
Answer & Analysis
Answer
B
Analysis
Question Analysis:
This question involves equilateral and right triangles.
The main focus is on using angle properties of an equilateral triangle and right triangles to find unknown angles.
Key Concept Explanation:
Equilateral Triangle Property:
An equilateral triangle has three equal angles, each measuring 60°.
Right Triangle Property:
A right triangle has one 90° angle, and the sum of the other two angles must be 90°.
Step-by-Step Solution:
Step 1: Find
- Since the upper triangle is equilateral, all its angles are 60°.
- The angle adjacent to (which is part of the equilateral triangle) is 60°.
- Since the given diagram contains a right angle next to , we use:
Step 2: Find
- The right triangle contains a 90° angle.
- Since we just found that , the remaining angle is:
Thus, we get
This question involves equilateral and right triangles.
The main focus is on using angle properties of an equilateral triangle and right triangles to find unknown angles.
Key Concept Explanation:
Equilateral Triangle Property:
An equilateral triangle has three equal angles, each measuring 60°.
Right Triangle Property:
A right triangle has one 90° angle, and the sum of the other two angles must be 90°.
Step-by-Step Solution:
Step 1: Find
- Since the upper triangle is equilateral, all its angles are 60°.
- The angle adjacent to
- Since the given diagram contains a right angle next to
Step 2: Find
- The right triangle contains a 90° angle.
- Since we just found that
Thus, we get
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