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In a triangle, if one angle is 90 degrees and the other two angles are equal, wh

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Question: In a triangle, if one angle is 90 degrees and the other two angles are equal, what is the measure of each of the equal angles?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 45 degrees

Solution: 

In a triangle, the sum of angles is 180 degrees. If one angle is 90 degrees, the other two angles must sum to 90 degrees. Therefore, each of the equal angles is 45 degrees.

In a triangle, if one angle is 90 degrees and the other two angles are equal, wh

Practice Questions

Q1
In a triangle, if one angle is 90 degrees and the other two angles are equal, what is the measure of each of the equal angles?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

In a triangle, if one angle is 90 degrees and the other two angles are equal, what is the measure of each of the equal angles?
  • Step 1: Understand that a triangle has three angles.
  • Step 2: Know that the total sum of the angles in a triangle is always 180 degrees.
  • Step 3: Identify that one angle in the triangle is 90 degrees (this is a right angle).
  • Step 4: Since one angle is 90 degrees, subtract this from 180 degrees to find the sum of the other two angles: 180 - 90 = 90 degrees.
  • Step 5: Recognize that the other two angles are equal, so we can call them both 'x'.
  • Step 6: Set up the equation: x + x = 90 degrees (because the two angles are equal).
  • Step 7: Simplify the equation: 2x = 90 degrees.
  • Step 8: Divide both sides of the equation by 2 to find the value of x: x = 90 / 2 = 45 degrees.
  • Step 9: Conclude that each of the equal angles measures 45 degrees.
  • Triangle Angle Sum Theorem – The sum of the interior angles of a triangle is always 180 degrees.
  • Properties of Isosceles Triangles – In an isosceles triangle, the angles opposite the equal sides are equal.
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