A right triangle has one angle that measures 90 degrees. What are the measures of the other two angles if the triangle is also isosceles?A) 45 degrees and 45 degreesB) 60 degrees and 30 degreesC) 70 degrees and 20 degreesD) 50 degrees and 40 degrees
Question
A right triangle has one angle that measures 90 degrees. What are the measures of the other two angles if the triangle is also isosceles?A) 45 degrees and 45 degreesB) 60 degrees and 30 degreesC) 70 degrees and 20 degreesD) 50 degrees and 40 degrees
Solution
In an isosceles right triangle, the two legs are of equal length. This means that the two non-right angles are also equal. Since the sum of all angles in a triangle is 180 degrees, and one angle is 90 degrees (as it's a right triangle), the other two angles must add up to 90 degrees.
Since these two angles are equal (as it's an isosceles triangle), each must be 90 degrees divided by 2, which is 45 degrees.
So, the measures of the other two angles are 45 degrees and 45 degrees.
Therefore, the correct answer is A) 45 degrees and 45 degrees.
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