Q9 of 69 Page 10

If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

Given bisector og the base angles of a triangle enclose an angle of 135^o

i.e. ∠BOC = 135^o

But,

135^o = 90^o + ∠A

∠A = 135^o – 90^o

∠A = 45^o (2)

= 90^o

Therefore, is right angled triangle right angled at A.

ABC is a triangle in which ∠A = 72°, the internal bisectors of angles B and C meet in O. Find the magnitude of ∠BOC.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

In a Δ ABC, ∠ABC =∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Shoe that ∠A =∠B =∠C = 60°.

Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than 60°?

(v) All angles less than 60°?

(vi) All angles equal to 60°?

Justify your answer in each case.