Math Problem Statement

Find the measure of each numbered angle.

Solution

The image shows a diagram with four numbered angles, and we are asked to find the measure of each angle. Here's how we can approach this:

Information given:

  • One of the angles is marked as 70°.
  • There is a right angle (90°) at the top left corner (between angle 1 and angle 2).
  • Angle 3 is adjacent to a 35° angle.
  • The angles appear to be part of a larger geometric figure, possibly involving triangles.

Step-by-step approach:

  1. Angle 1:

    • Angle 1 is part of a right triangle, and it is complementary to angle 2 (since the sum of the angles in a triangle is 180°, and one angle is 90°).
    • To find angle 1: Angle 1=90°70°=20°\text{Angle 1} = 90° - 70° = 20°.
  2. Angle 2:

    • Angle 2 and angle 1 form a right angle.
    • Therefore, Angle 2=90°\text{Angle 2} = 90°.
  3. Angle 3:

    • Angle 3 is adjacent to the 35° angle, and these two angles form a straight line (linear pair).
    • So, Angle 3=180°35°=145°\text{Angle 3} = 180° - 35° = 145°.
  4. Angle 4:

    • The total sum of the angles in a triangle is 180°.
    • Since we have a triangle formed by angles 4, 70°, and 35°, the sum of these angles should equal 180°.
    • To find angle 4: Angle 4=180°70°35°=75°\text{Angle 4} = 180° - 70° - 35° = 75°.

Final Results:

  • Angle 1 = 20°
  • Angle 2 = 90°
  • Angle 3 = 145°
  • Angle 4 = 75°

Would you like more details or have any other questions? Here are some related problems:

  1. What is the sum of angles in any triangle?
  2. How are complementary and supplementary angles defined?
  3. Can you explain what a linear pair of angles is?
  4. How do we calculate angles in any polygon?
  5. What is the relationship between interior and exterior angles in polygons?

Tip: Always remember that the sum of angles on a straight line is 180°, and the sum of angles in a triangle is always 180°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angles

Formulas

Sum of angles in a triangle = 180°
Sum of angles on a straight line = 180°
Complementary angles sum to 90°

Theorems

Angle Sum Theorem
Linear Pair Theorem

Suitable Grade Level

Grades 6-8