Math Problem Statement

Use the diagram and the given angle measure (m∠4 = 29°) to find the other three measures.

Solution

The image shows a pair of scissors, where angles are marked. Angle m4=29m\angle 4 = 29^\circ is given, and we need to find the other three angles (m1m\angle 1, m2m\angle 2, and m3m\angle 3).

Solution:

  • Angles 1\angle 1 and 3\angle 3 appear to be vertical angles, which means they are congruent (equal in measure). Therefore: m1=m3m\angle 1 = m\angle 3

  • Angles 2\angle 2 and 4\angle 4 are also vertical angles, meaning: m2=m4=29m\angle 2 = m\angle 4 = 29^\circ

  • The sum of the angles on a straight line is 180180^\circ. Since 1\angle 1 and 2\angle 2 are adjacent on the straight line formed by the scissors, we have: m1+m2=180m\angle 1 + m\angle 2 = 180^\circ Substituting m2=29m\angle 2 = 29^\circ: m1+29=180m\angle 1 + 29^\circ = 180^\circ m1=18029=151m\angle 1 = 180^\circ - 29^\circ = 151^\circ Thus: m1=151m\angle 1 = 151^\circ And since m1=m3m\angle 1 = m\angle 3, we also have: m3=151m\angle 3 = 151^\circ

Final answers:

  • m1=151m\angle 1 = 151^\circ
  • m2=29m\angle 2 = 29^\circ
  • m3=151m\angle 3 = 151^\circ

Would you like more details or have any questions?

Here are 5 related questions:

  1. What are vertical angles and why are they always congruent?
  2. Can angles in any other type of figure be considered vertical angles?
  3. How do we calculate unknown angles on a straight line?
  4. What is the sum of angles around a point?
  5. How do adjacent angles relate to complementary and supplementary angles?

Tip: Remember that vertical angles are always equal, and angles on a straight line sum to 180°, which is useful in many geometry problems.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Vertical Angles
Supplementary Angles

Formulas

m∠1 + m∠2 = 180° (adjacent angles on a straight line)
Vertical angles are congruent (m∠1 = m∠3, m∠2 = m∠4)

Theorems

Vertical Angles Theorem
Linear Pair Postulate

Suitable Grade Level

Grades 6-8