Math Problem Statement

find the missing angles

Find the missing angles.

Solution

In the given image, we are dealing with a transversal intersecting two parallel lines. When a transversal intersects two parallel lines, the corresponding angles are equal, and the alternate interior angles are equal.

From the image:

  1. Angle 1 is given as 5252^\circ.
  2. Angle 4 is a corresponding angle to angle 1, so angle 4 is also 5252^\circ.
  3. Angle 2 and angle 5 are alternate interior angles, so angle 2 is 4747^\circ.

Now, for triangle 2-3-5:

The sum of angles in a triangle is 180180^\circ: Angle 2+Angle 3+Angle 5=180\text{Angle 2} + \text{Angle 3} + \text{Angle 5} = 180^\circ 47+Angle 3+52=18047^\circ + \text{Angle 3} + 52^\circ = 180^\circ Angle 3=18099\text{Angle 3} = 180^\circ - 99^\circ Angle 3=81\text{Angle 3} = 81^\circ

So, the missing angles are:

  • Angle 4 = 5252^\circ
  • Angle 2 = 4747^\circ
  • Angle 3 = 8181^\circ

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles formed by transversal lines
Properties of triangles

Formulas

Sum of angles in a triangle: Angle 1 + Angle 2 + Angle 3 = 180°

Theorems

Corresponding angles are equal when a transversal intersects two parallel lines.
Alternate interior angles are equal when a transversal intersects two parallel lines.

Suitable Grade Level

Grades 7-10