finding missing angles in triangles worksheet answers house
The Correct Answer and Explanation is:
Worksheet Answers: The Geometry House
- Triangle A (Main Roof): The missing angle is 100°.
- Triangle B (Dormer Window): The missing angle is 30°.
- Triangle C (Gable Decoration): The missing angle is 55°.
Explanation: The Angle Sum Property of Triangles
To find the missing angles in the house diagram, we use a fundamental rule of geometry: The sum of the interior angles in any triangle always equals 180 degrees. This principle is the key to solving for any unknown angle when the other two are known. Let’s break down each triangle from the worksheet.
Triangle A: The Main Roof
- Given Information: This is an isosceles triangle, identified by the two equal base angles of 40° each.
- Principle: We apply the 180° rule. We know two angles, so we can set up an equation to find the third angle, which we’ll call x.
- Calculation:
Angle 1 + Angle 2 + Angle x = 180°
40° + 40° + x = 180°
80° + x = 180°
To isolate x, we subtract 80° from both sides:
x = 180° – 80°
x = 100° - Answer: The missing angle at the peak of the roof is 100°.
Triangle B: The Dormer Window
- Given Information: This is a right-angled triangle, indicated by the square symbol, which means one angle is exactly 90°. The other given angle is 60°.
- Principle: Even in a specialized triangle like a right-angled one, the sum of its angles is still 180°.
- Calculation:
Angle 1 + Angle 2 + Angle y = 180°
90° + 60° + y = 180°
150° + y = 180°
To find y, we subtract 150° from 180°:
y = 180° – 150°
y = 30° - Answer: The missing acute angle in the dormer window is 30°.
Triangle C: The Gable Decoration
- Given Information: This scalene triangle has two different angles provided: 75° and 50°.
- Principle: We once again use the angle sum property.
- Calculation:
Angle 1 + Angle 2 + Angle z = 180°
75° + 50° + z = 180°
125° + z = 180°
To solve for z, subtract 125° from 180°:
z = 180° – 125°
z = 55° - Answer: The third angle in the gable decoration is 55°
