Question

A triangle ABC is constructed with BC = 4.5 cm, AC = 4.5 cm and $\angle B={60}^{\circ }$. Then the measure of the angle A is

• A. 80${}^{\circ }$
• B. 90${}^{\circ }$
• C. 40${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

The correct option is D 60${}^{\circ }$

Step 1:
Draw a line segment of BC of length 4.5 cm.

Step 2:
Mark a ray BX making an angle 60${}^{\circ }$ at B.

Step 3:
With C as centre, draw an arc of radius of 4.5 cm to cut ray BX.

Step 4:
Mark the intersecting point as A and join CA to get the required $△$ABC.



From the above construction, we see that the measure of the third side is equal to 4.5 cm.

Hence, the triangle constructed is an equilateral triangle.

Since, in an equilateral triangle all the angles are equal hence, $\angle$A = $\angle$B = $\angle$C = 60 ${}^{\circ }$

Hence, $\angle$A = 60 ${}^{\circ }$