Question

An equilateral triangle and an isosceles triangle share a common side. What is the measure of angle ABC?

Answer 1

Answer:

Therefore ,the measure of angle ABC = 116°.

Step-by-step explanation:

Given:

Δ CBD is an Equilateral Triangle

BC = BD = CD

Δ ABD is an Isosceles Triangle

AB = BD

To Find:

m∠ ABC = ?

Solution:

Property For an Equilateral Triangle:

All the measure of Each of the angles angles of a triangle is 60°.

Δ CBD is an Equilateral Triangle   ..........Given

∴ m∠ CBD = 60° ....................( 1 )

Property For an Isosceles Triangle:

Any two of the base angles are equal.

Δ ABD is an Isosceles Triangle ................Given

∴ m∠ BAD = m∠ BDA = 62°  .....................( 2 )

Property of Triangle:

SUM of the measure of an angles of a triangle is 180°

In Δ BAD,

m∠ ABD + m∠ BAD + m∠ BDA = 180°

Substituting the values from equation ( 2 ) in it we get

m∠ ABD + 62 + 62 = 180

∴ m∠ ABD = 180 -124

∴ m∠ ABD = 56°     ................( 3 )

Now By angle addition property we have

m∠ ABC = m∠ ABD  + m∠ CBD

Substituting the values from equation 1 and equation 3 we get

∴ m∠ ABC = 56 + 60

∴ m∠ ABC = 116°

Therefore ,the measure of angle ABC = 116°.