Missing Angle of a Triangle Lesson

Lesson Overview

• What Is a Triangle?

Imagine you're building a triangular tent, but one side droops. You measured two of the angles, but something feels off. Without knowing the third angle, your structure collapses. That's the real-world power of geometry.

In this lesson, we'll uncover how to find the missing angle of a triangle, sharpening the geometric thinking you'll need in school, architecture, or even game design. Let's make sure no triangle-real or on paper-is ever incomplete again.

What Is a Triangle?

A triangle is a closed shape with three sides and three angles.

Angle Sum Property of a Triangle

Rule: The sum of all three interior angles in any triangle is always 180°.

Angle A+Angle B+Angle C=180∘\text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circAngle A+Angle B+Angle C=180∘

This rule helps us calculate a missing angle when two are known.

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Types of Triangles and Angle Relationships

Knowing the type helps you predict or verify angle values.

Steps to Calculate a Missing Angle

1. Identify the known angles.
   
2. Add the known angles together.
   
3. Subtract the sum from 180°.
   

Formula:

Missing angle=180∘−(Angle 1+Angle 2)\text{Missing angle} = 180^\circ - (\text{Angle 1} + \text{Angle 2})Missing angle=180∘−(Angle 1+Angle 2)

Worked Examples Based on Quiz Concepts

Let's break down similar cases found in the quiz.

Example 1: Triangle with angles 34° and 120°

Page 2 of the quiz shows this diagram.

Step-by-step:
34° + 120° = 154°
180° − 154° = 26°

Missing angle = 26°

Example 2: Right triangle with one 43° angle

Another question shows a right triangle with 90° and 43°.

Step-by-step:
90° + 43° = 133°
180° − 133° = 47°

Missing angle = 47°

Example 3: Given angle is 40.5°, others missing (partial data)

If another angle is known, apply the same rule:
180° − (40.5° + another angle) = missing angle

Example 4: One angle in a right triangle is 70°

Right triangle always includes 90°.

90° + 70° = 160°
180° − 160° = 20°

Third angle = 20°

Example 5: Two missing angles in a triangle

Given: One angle = 125°, one = 65° (from Page 3 diagram)

Add known angles:
125° + 65° = 190°

Wait! If the angles are external (as shown), convert to internal:

• External angles = 180° − internal angle
  Let's assume these are external.
  

So:
a = 180° − 125° = 55°
b = 180° − 65° = 115°

But if internal:
a + b = 180° − given angle

Encourage students to check whether angles are interior or exterior.

Common Mistakes to Avoid

Think Like a Mathematician

Can a triangle have two right angles?
No. Two 90° angles already equal 180°, leaving no space for a third angle.

If one angle is 90° and another is 45°, what type of triangle is it?
Right-angled triangle

Critical Thinking Prompt:

You're designing a ramp with triangular support. If you know one angle is 75°, how would you decide the rest to ensure balance?

Encourage students to visualize, sketch, and calculate before choosing.

8. Practice Table

Key Takeaway:

To find the missing angle of a triangle, always remember the 180-degree rule. Identify the triangle type to better predict angle relationships, especially in isosceles and right triangles. Use real-life examples to connect geometric logic with practical reasoning. Practice often to master the method, and be careful with diagrams to spot whether angles are internal or external.

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