Math Problem Statement

The given statement is: α = 90° - β. Is this true or false?

Solution

The given statement in the image is:

α=90β\alpha = 90^\circ - \beta

This is a right triangle, where we know that the sum of the angles in any triangle is always 180°. In a right triangle, one angle is 90°, and the other two angles (α and β) must sum to 90°. Therefore, the equation α+β=90\alpha + \beta = 90^\circ holds true, which can be rewritten as:

α=90β\alpha = 90^\circ - \beta

This confirms the statement is True.

Let me know if you'd like more details or if you have any questions!

Here are some related questions:

  1. How do we know that the sum of the angles in any triangle is 180°?
  2. Can you apply this rule to other types of triangles as well?
  3. How would you find the third angle in a triangle if you know two angles?
  4. What is the relationship between the sides of a right triangle and the angles?
  5. Can this rule (α=90β\alpha = 90^\circ - \beta) be applied to any right triangle?

Tip: In right triangles, you can use trigonometric ratios (sine, cosine, tangent) to find unknown angles and sides.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle Angles

Formulas

Sum of angles in a triangle = 180°
In a right triangle, one angle is 90°, and the other two add up to 90°.

Theorems

Angle sum property of triangles

Suitable Grade Level

Grades 6-8