Question

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

Answer 1

Answer:

135.gd right triangle 7xgsy ans and practice 55 no hexagon vall quarter gagev

Answer 2

Step-by-step explanation:

• To prove ∠C =90°

       In ΔABC bisector of base angle ∠A and ∠B meet at point O.

        It is given that ∠AOB = 135°

• We know the relation between ∠AOB and ∠C

        $\mathbf{\angle AOB =90^{\circ}+\frac{\angle C}{2}}$

        $\mathbf{135^{\circ}=90^{\circ}+\frac{\angle C}{2}}$

        $\mathbf{135^{\circ} - 90^{\circ}=\frac{\angle C}{2}}$

        $\mathbf{45^{\circ}=\frac{\angle C}{2}}$

        So

        ∠C = 90°     Proved