Question

A $∆ABC$can be constructed when $AC=8cm,$$m\angle A={60}^o$and $m\angle B={50}^o$using the _________ criterion.

• A. $ASA$
• B. $SAS$

Answer 1

The correct option is A

$ASA$

Step-1: Given Information

$AC=8cm,$(one side of the triangle)

$m\angle A={60}^o$

$m\angle B={50}^o$

Step-2: Find the angle $\angle C$

$\angle A+\angle B+\angle C={180}^o$ ( sum of interior angles of a triangle)

${60}^o+{50}^0+\angle C={180}^o$

${110}^o+\angle C={180}^o$

$\angle C={180}^o-{110}^0$

$\angle C={70}^o$

Step-3: Constructing a triangle

We can Construct a triangle if two angles and a side containing them are given.

Here, Two angles are $m\angle A={60}^o$$,m\angle C={70}^o$and the side containing them is $AC=8cm,$

Hence, Triangle $∆ABC$can be constructed by $ASA$