Question

ABCD is a parallelogram. Find the measure of <A? 40 120 20 160

Answer 1

`/_A=20^circ`

Explanation:

In a parallelogram opposite angles are equal ;
so `/_B=/_D`
and therefore
`color(white)("XXX")7x+13=8x-8`
`color(white)("XXX")rarr x=21`
and
`color(white)("XXX")/_B=7 * 21+13=160^circ`
`color(white)("XXX")/_D=8 * 21 -8 =160^circ`

`color(white)("XXX")/_B+/_D=320^circ`

Since the interior angles of a parallelogram add up to `360^circ`
#color(white)("XXX")/_A + /_C +/_B +/_D=360^circ

`color(white)("XXX")/_A+/_C+320^circ=360^c`

`color(white)("XXX")/_A+/_C=40^circ`

and since `/_A` and `/_C` are opposite angles
`color(white)("XXX")/_C=/_A`
and
`color(white)("XXX")2 * /_A=40^circ`

`color(white)("XXX")rArr /_A=20^circ`

Answer 2

`m/_A=20^@`

Explanation:

As oppositeangles of a parallelogram are equal hence,

`8x-8=7x+13`

or `8x-7x=13+8`

or `x=21`

Hence `m/_B=7xx21+13=160^@`

Now as adjacent angles of a parallelogram are supplementary,

`m/_A=180^@-160^@=20^@`