Math Problem Statement

A student is trying to construct triangles using four different sets of angles. The angles in each set are given below. Which set will form a triangle?

Solution

The question asks which set of angles can form a triangle. To form a triangle, the sum of the three angles must always equal 180°. Let’s check each set of angles:

  1. 45°, 65°, 70°: 45+65+70=180°(This forms a triangle.)45 + 65 + 70 = 180° \quad (\text{This forms a triangle.})

  2. 50°, 50°, 50°: 50+50+50=150°(This does not form a triangle.)50 + 50 + 50 = 150° \quad (\text{This does not form a triangle.})

  3. 90°, 90°, 90°: 90+90+90=270°(This does not form a triangle.)90 + 90 + 90 = 270° \quad (\text{This does not form a triangle.})

  4. 150°, 110°, 100°: 150+110+100=360°(This does not form a triangle.)150 + 110 + 100 = 360° \quad (\text{This does not form a triangle.})

The correct set that forms a triangle is 45°, 65°, 70°.

Would you like a deeper explanation, or have any questions?

Here are 5 related questions:

  1. What is the sum of the interior angles of a triangle?
  2. Can a triangle have more than one right angle?
  3. What is an equilateral triangle, and how do its angles compare?
  4. How can you identify if three given angles can form a triangle?
  5. What are the different types of triangles based on angles?

Tip: Always remember that the sum of angles in a triangle is 180°, regardless of the triangle's type.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8