Math Problem Statement

In the figure below, m∠1 = 69°. Find m∠2.

Solution

In the given figure, 1\angle 1 and 2\angle 2 are part of a linear pair. This means the two angles are adjacent and form a straight line, so their measures sum up to 180180^\circ.

We are given that the measure of 1=69\angle 1 = 69^\circ. To find 2\angle 2, we can use the following equation:

m1+m2=180m \angle 1 + m \angle 2 = 180^\circ

Substituting the known value:

69+m2=18069^\circ + m \angle 2 = 180^\circ

Solving for m2m \angle 2:

m2=18069=111m \angle 2 = 180^\circ - 69^\circ = 111^\circ

Thus, m2=111m \angle 2 = 111^\circ.

Would you like further details on this solution or have any other questions?

Here are 5 related questions to explore:

  1. What is a linear pair of angles?
  2. How are supplementary angles defined?
  3. Can two obtuse angles form a linear pair?
  4. What other angle relationships exist besides linear pairs?
  5. How do adjacent angles differ from linear pairs?

Tip: When dealing with linear pairs, remember that the angles will always sum to 180180^\circ, as they form a straight line.

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Math Problem Analysis

Mathematical Concepts

Linear Pair
Supplementary Angles

Formulas

m∠1 + m∠2 = 180°

Theorems

Linear Pair Theorem

Suitable Grade Level

Grades 6-8