Question

In the following figure `AB`||`DC`. Find `x`?

Answer 1

`m/_x=75^@`

Explanation:

As `AB`||`DC`, `m/_BAD+m/_ADC=180^@`

but `m/_ADC=45^@`

hence `m/_BAD=180^@-45^@=135^@`

but `m/_BAC=60^@`

Hence `m/_x=135^@-60^@=75^@`

Answer 2

`x=75^@`

Explanation:

`"angle BAC "=" angle ACD"larrcolor(blue)" alternate angles"`

`rArr"angle ACD "=60^@`

`"sum of the angles in triangle CAD "=180^@`

`rArr"angle CAD "=x=180^@-(60+45)^@=75^@`