Question 632601
What kind of angle pair are the the acute angles of a right triangle?
The expected answer must be {{{highlight(complementary)}}}
Because their measures plus the measure of the right angle must add up to {{{180^o}}},
the measures of the acute angles must add up to a right angle ({{{180^o-90^o=90^o}}} in degrees or {{{pi/2}}} 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^o}}}), each of those acute angles measures {{{highlight(45^o)}}} (or {{{highlight(pi/4)}}} 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^o}}} --> {{{x=90^o/3}}} --> {{{highlight(x=30^o)}}} and
{{{2x=2*30^o}}} --> {{{highlight(2x=60^o)}}}