# NCERT Solutions Class 8 Mathematics Solutions for Exercise 4.3 in Chapter 4 - Practical Geometry

Question 1 Exercise 4.3

MO = 6 cm

OR = 4.5 cm

\begin{array}{l} \angle \mathrm{M}=60^{\circ} \\ \angle \mathrm{O}=105^{\circ} \\ \angle \mathrm{R}=105^{\circ} \end{array}

PL = 4 cm

LA = 6.5 cm

\begin{array}{l} \angle \mathrm{P}=90^{\circ} \\ \angle \mathrm{A}=110^{\circ} \\ \angle \mathrm{N}=85^{\circ} \end{array}

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

\angle \mathrm{R}=85^{\circ}

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

(i) Rough Figure:

(1) Draw a line segment MO of 6 cm and an angle of 105^{\circ} at point O. As vertex R is 4.5 cm away from the vertex O, cut a line segment OR of 4.5 cm from this ray.

(2) Again, draw an angle of 105^{\circ} at point R.

(3) Draw an angle of 60^{\circ} at point M. Let this ray meet the previously drawn ray from R at point E.

(ii) The sum of the angles of a quadrilateral is 360^{\circ}.

\begin{array}{l} \angle \mathrm{P}+\angle \mathrm{L}+\angle \mathrm{A}+\angle \mathrm{N}=360^{\circ} \\ 90^{\circ}+\angle \mathrm{L}+110^{\circ}+85^{\circ}=360^{\circ} \\ 285^{\circ}+\angle \mathrm{L}=360^{\circ} \\ \angle \mathrm{L}=360^{\circ}-285^{\circ}=75^{\circ} \end{array}

Rough figure :

(1) Draw a line segment PL of 4 cm and draw an angle of 75^{\circ} at point L. As vertex A is 6.5 cm away from vertex L, cut a line segment LA of 6.5 cm from this ray.

(2) Again draw an angle of 110^{\circ} at point A.

(3) Draw an angle of 90^{\circ} at point P. This ray will meet the previously drawn ray from A at point N.

(iii) Rough Figure:

(1) Draw a line segment HE of 5 cm and an angle of 85^{\circ} at point E. As vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray.

(2) Vertex R is 6 cm and 5 cm away from vertex H and A respectively. By taking radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will be intersecting each other at point R.

(iv) Rough Figure:

(1) Draw a line segment OK of 7 cm and an angle of 90^{\circ} at point K. As vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray.

(2) Vertex Y is 5 cm and 7 cm away from vertex O and A respectively. By taking radius as 5 cm and 7 cm, draw arcs from point O and A respectively. These will be intersecting each other at point Y.

(3) Join Y to A and O.

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