Which of the following statement(s) given below is / are TRUE based on the figure given below:   A: ∠BAC + ∠ABC > ∠ACD B: If ∠ACB > 80°, then ∠BAC + ∠ABC must be smaller than 100°. C: If ∠ACD = 80°, then ∆ABC must be an acute angle triangle.

Which of the following statement(s) given below is / are TRUE based on the figure given below:   A: ∠BAC + ∠ABC > ∠ACD B: If ∠ACB > 80°, then ∠BAC + ∠ABC must be smaller than 100°. C: If ∠ACD = 80°, then ∆ABC must be an acute angle triangle. Correct Answer B

GIVEN:

Three statements.

CONCEPT:

Geometry

CALCULATION:

A:

We know that:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠BAC + ∠ABC = ∠ACD

B:

We know that:

∠BAC + ∠ABC = ∠ACD

⇒ ∠ACB = 180° - ∠ACD

⇒ 180° - ∠ACD > 80°

⇒ 100° > ∠ACD

⇒ ∠BAC + ∠ABC < 100°

C:

∠ACD = 80°

⇒ ∠ACD + ∠ACB = 180°

⇒ ∠ACD = 100°

We can say that one angle of a triangle is obtuse angle. So, ∆ABC cannot be an acute angle triangle.