Question

How many degrees is THETA?

NOTE: Diagram is not to scale.
Give numerical answer only, no units.

Answer 1

104

Explanation:

All interior angles of triangles add up to 180. So, using the information we are given we can find the missing angle, theta. One way to do this by setting up an equation like 31+45+θ=180. Solve this to get 104, your final answer. If you want, you can check your work by plugging in 104, 31+45+104=180. Since 180=180, 104 must be correct.

Answer 2

θ = 104°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

• All angles in a triangle add up to 180°

Explanation:

Step 1: Define

Identify and set up

m∠A = 31°

m∠B = θ

m∠C = 45°

θ + 31° + 45° = 180°

Step 2: Find θ

1. Add: θ + 76° = 180°
2. [Subtraction Property of Equality] Subtract 76° on both sides: θ = 104°