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)
Practice Questions
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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)
Angle C is 45 degrees and angle D is 90 degrees.
Angle C is 90 degrees and angle D is 45 degrees.
Angle C is 135 degrees and angle D is 135 degrees.
Angle C is 180 degrees and angle D is 0 degrees.
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.
Questions & Step-by-step Solutions
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Q
Q: 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)
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.
Steps: 8
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.
