Question

In △ABC, if D is the midpoint of AC and AD = BD = CD, then ∠ABC =

a) 80°
b) 120°
c) 90°
d) 45°


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Answer 1

Given :

In △ABC, if D is the midpoint of AC and AD = BD = CD, then ∠ABC =

To Find :

The value of ∠ABC.

Solution :

Given that,

• In △ABC, if D is the midpoint of AC
• AD = BD = CD

Now, take angle as 90°

$\sf\ ⇒ \: \: \angle A \: \: + \: \angle B \: \: + \: \angle C \: \: = \: 180 \degree \: ( \: Angle \: sum \: property \: )$

$\sf\ ⇒ \: \: x \degree \: + \: \: 90 \degree \: \: + \: x \degree \: \: = \: \: 180 \degree$

$\sf\ ⇒ \: \: x \: \: = \: \: 180 \: \: - \: \: 90$

${\red{\sf{ ⇒}}} \: \: \: {\boxed{\sf{\red{ \: \: x \: \: = \: \: 90 \degree}}}}$ $\:$(Option : C)

$\tiny$

${{\sf{\underline{\therefore \: Hence, \: Solved!}}}}^{\bf\ VIJAY}$