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# 6.Find the angle measure x in the following figures.

(a) As we know the sum of interior angles of a quadrilateral is $$360^{\circ}$$.
∴ $$x+ 120^{\circ} +130^{\circ} +50^{\circ}= 360^{\circ}$$

$$\Rightarrow x+300^{\circ} = 360^{\circ}$$

$$\Rightarrow x=360^{\circ} - 300^{\circ}= 60^{\circ}$$

(b) As we know the sum of interior angles of a quadrilateral is $$360^{\circ}$$.
∴ $$x+ 70^{\circ} +60^{\circ} +90^{\circ}= 360^{\circ}$$

$$\Rightarrow x+220^{\circ} = 360^{\circ}$$

$$\Rightarrow x=360^{\circ} - 220^{\circ}= 140^{\circ}$$

(c) As we see the given figure with 5 sides, so the sum of interior angles of this polygon is =$$(n-2) \times 180^{\circ} = 3 \times 180^{\circ}=540^{\circ}$$

So in the figure we have ,

$$m∠1 + 60^{\circ} =180^{\circ} \quad$$[Angle of straight line is $$180^{\circ}$$]

$$\Rightarrow m∠1=180^{\circ}- 60^{\circ} =120^{\circ}$$

and also, $$m∠2 + 70^{\circ} =180^{\circ} \quad$$[Angle of straight line is $$180^{\circ}$$]

$$\Rightarrow m∠2=180^{\circ}- 70^{\circ} =110^{\circ}$$

Therefore, the sum of internal angles:

$$\qquad m∠1+m∠1+x+30^{\circ} +x= 540^{\circ}$$

$$\Rightarrow 120^{\circ}+110^{\circ}+2x+30^{\circ}=540^{\circ}$$

$$\Rightarrow 2x+260^{\circ}=540^{\circ}$$

$$\Rightarrow 2x=540^{\circ}-260^{\circ}=280^{\circ}$$

$$\Rightarrow x=\frac{280^{\circ}}{2}=140^{\circ}$$

(d) As we see the given figure with 5 sides, so the sum of interior angles of this polygon is =$$(n-2) \times 180^{\circ} = 3 \times 180^{\circ}=540^{\circ}$$

Therefore, the sum of internal angles:

$$\qquad x+x+x+x+x= 540^{\circ}$$

$$\Rightarrow 5x= 540^{\circ}$$

$$\Rightarrow x=\frac{280^{\circ}}{5}=108^{\circ}$$