Question

Help,anyone can help me do quetion.​

Answer 1

(a) x =
`128^(o)`

(b) x =
`74^(o)`

Explanation:

A. sum of angles in a polygon = (n - 2) 180

The polygon given is an irregular pentagon, where n = 5

So that;

sum of angles in a pentagon = (5 - 2) 180

= 3 x 180

=
`540^(o)`

Thus,

x + 90 + 76 + 110 + 136 =
`540^(o)`

x + 412 =
`540^(o)`

x =
`540^(o)` - 412

x =
`128^(o)`

B. The polygon given is an irregular pentagon, where n = 5.

Let the supplementary angle with angle 38 be represented by y,

y + 38 = 180

y = 180 - 38

=
`142^(o)`

y =
`142^(o)`

Let the supplementary angle with x be represented by z, so that;

z + 72 + 120 + 100 + 142 =
`540^(o)`

z + 434 =
`540^(o)`

z =
`540^(o)` - 434

=
`106^(o)`

z =
`106^(o)`

But, x + z =
`180^(o)`

Then;

x +
`106^(o)` =
`180^(o)`

x =
`180^(o)` -
`106^(o)`

=
`74^(o)`

x =
`74^(o)`