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Help,anyone can help me do quetion.​

Help,anyone can help me do quetion.​-example-1
User Bajohns
by
4.2k points

1 Answer

1 vote

Answer:

(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)

User Jorge Quintana
by
4.9k points