Answer: The measure of angle A is 60 degree.
Explanation:
It is given that the Triangles A B E and D C E share vertex E. Angle B is 18 degrees. Angle C is 43 degrees. Angle D is 35 degrees.
According to angle sum property, the sum of angles of a triangle is always 180 degree.
In triangle CDE,
[tex]\angle ECD+\angle CDE+\angle DEC=180^{\circ}[/tex]
[tex]43^{\circ}+35^{\circ}+\angle DEC=180^{\circ}[/tex]
[tex]78^{\circ}+\angle DEC=180^{\circ}[/tex]
[tex]\angle DEC=180^{\circ}-78^{\circ}[/tex]
[tex]\angle DEC=102^{\circ}[/tex]
According to opposite vertical angle property.
[tex]\angle AEB=\angle DEC[/tex]
[tex]\angle AEB=102^{\circ}[/tex]
Use angle sum property is triangle ABE.
[tex]\angle ABE+\angle BEA+\angle EAB=180^{\circ}[/tex]
[tex]\angle ABE+102^{\circ}+18^{\circ}=180^{\circ}[/tex]
[tex]\angle ABE+120^{\circ}=180^{\circ}[/tex]
[tex]\angle ABE=60^{\circ}[/tex]
Therefore, the measure of angle A is 60 degree.
