Question

The dotted line represents the line of symmetry of the isosceles triangle abc where ab is equal to AC and angle abc is equal to 40 degree and obese equal to 4.5 cm find the angle bao

Answer 1

Refer to the attached image.

Consider the isosceles triangle ABC in which AB = AC.

Given: $\angle ABC = \angle ACB = 40^\circ$

Consider triangle ABC,

By using the angle sum property of a triangle which states

"The sum of all the angles of the triangle is 180 degrees".

$\angle ABC + \angle ACB + \angle BAC = 180^\circ$

$40^\circ + 40^\circ + \angle BAC = 180^\circ$

$80^\circ + \angle BAC = 180^\circ$

$\angle BAC = 180^\circ - 80^\circ$

$\angle BAC = 100^\circ$

Since, OA is the line of symmetry of the triangle which means it divides the triangle into two equal parts.

Hence, it bisects the angle A into two equal parts.

$\angle BAO = \frac{1}{2} \times \angle BAC$

$\angle BAO = \frac{1}{2} \times 100^\circ$

$\angle BAO = 50^\circ$

Therefore, the measure of angle BAO is 50 degrees.

Answer 2

Step-by-step explanation:

Refer to the attached image.

Consider the isosceles triangle ABC in which AB = AC.

Given: \angle ABC = \angle ACB = 40^\circ∠ABC=∠ACB=40

∘

Consider triangle ABC,

By using the angle sum property of a triangle which states

"The sum of all the angles of the triangle is 180 degrees".

\angle ABC + \angle ACB + \angle BAC = 180^\circ∠ABC+∠ACB+∠BAC=180

∘

40^\circ + 40^\circ + \angle BAC = 180^\circ40

∘

+40

∘

+∠BAC=180

∘

80^\circ + \angle BAC = 180^\circ80

∘

+∠BAC=180

∘

\angle BAC = 180^\circ - 80^\circ∠BAC=180

∘

−80

∘

\angle BAC = 100^\circ∠BAC=100

∘

Since, OA is the line of symmetry of the triangle which means it divides the triangle into two equal parts.

Hence, it bisects the angle A into two equal parts.