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°.
