Scenario: Architecture Design - Learn about angle relationships through building and design projects!
You're designing a modern building with intersecting walls. The architect needs to know the angles where walls meet to ensure proper structural support and aesthetic appeal.
Design Challenge:
Two walls intersect at a point. One angle formed is 65°. Find all other angles at this intersection.
Intersecting walls create four angles at the intersection point
Vertical Angles Theorem: Vertical angles are always equal.
When two lines intersect, the angles opposite each other are called vertical angles and they have the same measure.
Given: One angle is 65°
Step 1: Find the vertical angle
Vertical angles are equal, so the opposite angle is also 65°
Step 2: Find the supplementary angles
180° - 65° = 115°
Answer: The four angles are 65°, 65°, 115°, and 115°
Two angles that add up to 90°
Example: 30° + 60° = 90°
Two angles that add up to 180°
Example: 120° + 60° = 180°
In a building design, two support beams meet at a 45° angle. Find the complementary and supplementary angles.
Complementary angle: 90° - 45° = 45°
Supplementary angle: 180° - 45° = 135°
Two lines intersect. One angle is 72°. Find all four angles formed.
Your solution:
Two complementary angles are in the ratio 2:3. Find the measure of each angle.
Your calculation: