Math Problem Statement

Find the missing angle in a triangle where two angles are 40° and 70°.

Solution

To find the missing angle 1\angle 1 in a triangle, we can use the fact that the sum of all angles in any triangle is always 180180^\circ.

Given:

  • One angle is 4040^\circ,
  • Another angle is 7070^\circ,
  • Let the missing angle be 1\angle 1.

We use the formula: 1=180(40+70)\angle 1 = 180^\circ - (40^\circ + 70^\circ) 1=180110=70\angle 1 = 180^\circ - 110^\circ = 70^\circ

So, 1=70\angle 1 = 70^\circ.

Would you like more details on the calculation? Here are some related questions:

  1. Why do the angles of a triangle always add up to 180 degrees?
  2. What is the relationship between angles in different types of triangles (e.g., equilateral, isosceles)?
  3. How do supplementary angles relate to triangles?
  4. Can you solve for missing angles in quadrilaterals similarly?
  5. How can exterior angles of a triangle help in finding interior angles?

Tip: Always double-check your angle sums when solving for missing angles in triangles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties
Angle Sum of a Triangle

Formulas

Sum of angles in a triangle = 180°
Missing angle = 180° - (sum of given angles)

Theorems

Angle Sum Theorem for Triangles

Suitable Grade Level

Grades 6-8