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In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, wha

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Question: In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)

Options:

  1. Angle C is 45 degrees and angle D is 90 degrees.
  2. Angle C is 90 degrees and angle D is 45 degrees.
  3. Angle C is 135 degrees and angle D is 135 degrees.
  4. Angle C is 180 degrees and angle D is 0 degrees.

Correct Answer: Angle C is 135 degrees and angle D is 135 degrees.

Exam Year: 2023

Solution: 

In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.

In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, wha

Practice Questions

Q1
In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
  1. Angle C is 45 degrees and angle D is 90 degrees.
  2. Angle C is 90 degrees and angle D is 45 degrees.
  3. Angle C is 135 degrees and angle D is 135 degrees.
  4. Angle C is 180 degrees and angle D is 0 degrees.

Questions & Step-by-Step Solutions

In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
  • Step 1: Understand that a quadrilateral has four angles: A, B, C, and D.
  • Step 2: Know that the sum of all angles in a quadrilateral is always 360 degrees.
  • Step 3: Identify the given angles: angle A is 90 degrees and angle B is 45 degrees.
  • Step 4: Add the known angles together: 90 + 45 = 135 degrees.
  • Step 5: Subtract the sum of the known angles from 360 degrees to find the sum of angles C and D: 360 - 135 = 225 degrees.
  • Step 6: Since angles C and D must add up to 225 degrees, we can assume they are equal for simplicity: C = D.
  • Step 7: Divide 225 degrees by 2 to find the measure of each angle: 225 / 2 = 112.5 degrees.
  • Step 8: Conclude that angle C and angle D can be 112.5 degrees each, or other combinations that add up to 225 degrees.
  • Sum of Angles in a Quadrilateral – The total sum of the interior angles in any quadrilateral is always 360 degrees.
  • Properties of Angles – Understanding how to calculate unknown angles based on known angles in geometric figures.
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