# Construct the following and give justification :A triangle if its perimeter is 10.4 cm and two angles are $45^{\circ}$ and $120^{\circ}$.

Steps of Construction :

1. Draw a line PQ = 10.4 cm
2. Draw line PR with $45^{\circ}$ angle at P.

$\angle RPQ=45^{\circ}$

1. Draw line QS with $120^{\circ}$ angle at Q.

$\angle SPQ=120^{\circ}$

3.         Bisect $\angle RPQ$ and $\angle SPQ$ and then let their bisectors meet at point A

4.         Bisect line AQ and AP which meets PQ at C and B respectively.

5.         Join A with B and C.

ABC is the required triangle.

Justification:

Since B and C lies on PQ

Hence, PB + BC + CQ = AB + BC + AC = PQ

$\angle BAP= \angle APB$  …..(i)                    { in DAPB, AB = PB}

$\angle ABC= \angle BPA+ \angle APB$             [$\angle ABC$ is an exterior angle of DAPB]

$\angle ABC= 2 \angle APB = \angle RPQ$          {from (i),$\angle RPQ= \angle RPA + \angle APQ$}

Also,  $\angle CAQ = \angle AQC$                        [in DAQC ; AC = CQ]

$\angle ACB = \angle CAQ + \angle AQC$            [$\angle ACB$ is exterior angle of DAQC]

$\angle ACB = 2 \angle CAQ = \angle SQP$         [\AQ is a bisector of $\angle SQP$]

### Preparation Products

##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-