Question

Find the measures of each angle (please show work)

Answer 1

Part 11)
`m<1=135\°`,
`m<2=135\°`,
`m<3=45\°`

Part 12)
`m<1=90\°`,
`m<2=25\°`

Explanation:

Part 11) we know that

Find the measure angle 3

The base angles of an isosceles trapezoid are equal in measure

so

`m<3=45\°`

Find the measure of angle 1

`m<1+45\°=180\°` -----> by supplementary angles

`m<1=180\°-45\°=135\°`

Find the measure of angle 2

`m<2+m<3=180\°` -----> by supplementary angles

`m<2+45\°=180\°`

`m<2=180\°-45\°=135\°`

Part 12) we know that

In a Kite the diagonals are perpendiculars

so

`m<1=90\°`

and

`m<2+65\°=90\°` ------> by complementary angles

`m<2=90\°-65\°=25\°`