SOLUTION: what kind of angle pair are the acute angles of a right triangle? What is the measuire of the smallest angle in an isosceles right triangle? The ratio of the angles of a triangle

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Question 632601: what kind of angle pair are the acute angles of a right triangle?
What is the measuire of the smallest angle in an isosceles right triangle?
The ratio of the angles of a triangle is 1:2:3.What are the measures of the angles ?
Answer by KMST(5328) About Me  (Show Source):
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What kind of angle pair are the the acute angles of a right triangle?
The expected answer must be highlight%28complementary%29
Because their measures plus the measure of the right angle must add up to 180%5Eo,
the measures of the acute angles must add up to a right angle (180%5Eo-90%5Eo=90%5Eo in degrees or pi%2F2 in radians).
A pair of angles that add up to a right angle is called complementary, so the acute angles of a right triangle are complementary.

What is the measure of the smallest angle in an isosceles right triangle?
Besides its right angle, an isosceles right triangle has two congruent acute angles opposite congruent legs. Because their measures must add up to a right angle (90%5Eo), each of those acute angles measures highlight%2845%5Eo%29 (or highlight%28pi%2F4%29 in radians).

The ratio of the angles of a triangle is 1:2:3.What are the measures of the angles ?
The largest angle must be the right angle. If the angles are in the ratio 1:2:3,
their measures would be x, 2x, and 3x,
with 3x=90%5Eo --> x=90%5Eo%2F3 --> highlight%28x=30%5Eo%29 and
2x=2%2A30%5Eo --> highlight%282x=60%5Eo%29