Question

Determine the measure of the angles.
m<1 =
m<2 =
m<3 =

Answer 1

58° , 122° , 29°

Explanation:

The triangle on the left has 2 congruent sides thus is isosceles.

Then the 2 base angles are congruent, so

∠ 1 =
`(180-64)/(2)` =
`(116)/(2)` = 58°

∠ 2 and 58° are adjacent angles and supplementary, that is

∠ 2 + 58° = 180° ( subtract 58° from both sides )

∠ 2 = 122°

The triangle on the right has 2 congruent sides and is isosceles

Then the 2 base angles are congruent, so

∠ 3 =
`(180-122)/(2)` =
`(58)/(2)` = 29°