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Answer :

(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:

\(\qquad x+x+x+x+x= 540^{\circ}\)

\(\Rightarrow 5x= 540^{\circ}\)

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

- 1. Given here are some figures : Classify each of them on the basis of the following : (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon
- 2.How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle.
- 3.What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and j try!)
- 4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n
- 5.What is a regular polygon? State the name of a regular polygon of (i) 3 slides (ii) 4 slides (iii) 6 slides
- 7. (a) Find x + y + z (b) Find x + y + z + w

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