Name: Construction of Triangle When Base Angles and Perimeter Is Given
Uploaded: 2019-07-19
Duration: 5 min 46 s
Description: A perimeter and the three angles are a must for a triangle to exist. But you don't necessarily need all of these to construct a triangle. Let’s learn how in...

Question

Construct the angle

15 °

.

Accepted Answer

We can write the given angle as,

$15 ° = \frac{1}{2} \times 30 ° = \frac{1}{2} \times \frac{1}{2} \times 60 °$

So, to make $15 °$ , we need to make $60 °$ and then bisect it twice.

Step of construction:

$1 .$ Draw a ray $O A$ .

$2 .$ Taking $O$ as the centre and any radius, draw an arc cutting $O A$ at $B$ .

$3 .$ Now, with $B$ as the centre, and same radius as before, draw another arc intersecting the previously drawn arc at point $C$ .

$4 .$ Draw ray $OD$ passing through $C$ .

Thus, $∠ A OD = 60 °$ .

Now we bisect $∠ AOD$ twice.

That is, $60 ° \to 30 ° \to 15 °$

$5 .$ Taking $C$ and $B$ as the centres, with radius more than $\frac{1}{2}$ $\overset{⏜}{CB},$ draw two arcs intersecting each other at a point and draw $OE$ through the intersecting point.

Thus, $∠ E OA = 30 °$

Now we need to bisect $∠ E OA$ , i.e. $\frac{30 °}{2} = 15 °$

$6 .$ Mark point $Q$ where $OE$ intersects the arc.

$7 .$ Taking $Q$ and $B$ as the centres, with radius more than $\frac{1}{2} \overset{⏜}{QB}$ , draw arcs intersecting at $R$ .

Thus, $∠ A O R = 15 °$

Thus, the given angle is constructed.

Construct the angle $15 °$ .

Important Questions on Constructions

Learn and Prepare for any exam you want !

Construct the angle 15°.

Important Questions on Constructions

Learn and Prepare for any exam you want !

Construct the angle $15 °$ .