Question

Help,anyone can help me do quetion.​

Answer 1

Answer:

(a) x = $128^{o}$

(b) x = $74^{o}$

Step-by-step 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 = $74^{o}$