Question

In the triangle ABC, AD = BD = CD. What is the


size of angle BAC?

Answer 1

Hello!

Answer:

`\Large \boxed{\sf 60^(\circ)}`

Explanation:

→ We want to find the angle BAC.

→ We know that AD = BD = CD.

→ Here is our triangle:

A

/\
/ \
/ \
/ \

B C

→ This triangle is equilateral because its 3 sides are equal.

→ We know that the angles of an equilateral triangle are equal.

→ Let x be an angle of our triangle.

- The sum of the angles of the triangle = x + x + x = 3x

- The sum of the angles of the triangle = 180°

So we have this equation:

`\sf 3x = 180`

→ Let's solve this equation to find the value of the angle BAC:

◼ Divide both sides by 3:

`\sf (3x)/(3) = (180)/(3)`

◼ Simplify both sides:

`\boxed{\sf x = 60}`

Conclusion:

The angle BAC is equal to 60°.