Name: Construction of Angles Using Protractor
Uploaded: 2019-07-19
Duration: 4 min 7 s
Description: We know that an angle is formed when two rays join at a common point. In this video session, learn how to construct angles using a basic geometry tool called a protractor.

Question

Construct

∠ A O B = 45 °

by using a ruler and a pair of compasses. Take a point

P

on oB such that

O P = 5 cm

. Draw the perpendicular on

P

to

O B

.

Accepted Answer

Steps of construction are as follows:

Draw a line and name it $\vec{O B}$ . Mark a point on $\vec{O B}$ such that $O P = 5 cm$ .

With $O$ as a centre and any convenient radius draw an arc cutting $\vec{O B}$ at $Q$ .

With $Q$ as centre and the same radius, draw an arc cutting the first arc at $R$ .

With $R$ as a centre and the same radius, draw an arc cutting the first arc at $S$ .

With $R$ and $S$ as centre and radius more than half of $R S$ , draw two arcs cutting each other at $T$ . Join $T O$ with dotted lines $∠ T O B = 90 °$ .

Measure the angle of $Q O T$ using compass. With $Q$ as centre and measured radius draw an arc cutting $\vec{O T}$ at $U$ .

With $Q$ and $U$ as centre and same measured radius, draw two arcs cutting each other at $V$ . Join $O$ and $V$ such that $∠ V O B = 45 °$ .

With $P$ as centre and any convenient radius draw an arc cutting $O B$ at $X$ .

With $X$ as a centre and any convenient radius draw an arc cutting the first arc at $Y$ .

With $Y$ as a centre and the same radius, draw an arc cutting the first arc at $Z$ .

With $Y$ and $Z$ as centre and radius more than half of $Y Z$ , draw two arcs cutting each other at $E$ . Therefore, $E P$ is perpendicular to $O P$ .

Extend $\vec{O U}$ and $\vec{P Q}$ then they intersect at point $A$ . Therefore, $∠ A O P = ∠ A O B = 45 °$ and $∠ A P O = 90 °$ .

Construct $∠ A O B = 45 °$ by using a ruler and a pair of compasses. Take a point $P$ on oB such that $O P = 5 cm$ . Draw the perpendicular on $P$ to $O B$ .

Important Questions on Construction of Angles

Learn and Prepare for any exam you want !

Construct ∠AOB=45° by using a ruler and a pair of compasses. Take a point P on oB such that OP=5 cm. Draw the perpendicular on P to OB.

Important Questions on Construction of Angles

Learn and Prepare for any exam you want !

Construct $∠ A O B = 45 °$ by using a ruler and a pair of compasses. Take a point $P$ on oB such that $O P = 5 cm$ . Draw the perpendicular on $P$ to $O B$ .