Answer:
Therefore, the measure of an acute base angle of the trapezoid are
[tex]\angle A=\angle B=67\°[/tex]
Step-by-step explanation:
Given:
Consider a Triangle ΔABC,with vertex angle as ∠A,
∠ A = 46°
DECB is an Isosceles trapezoid is part of an Isosceles triangle,
To Find:
∠ B = ∠C = ?
Solution:
As the Triangle,ΔABC is an Isosceles Triangle
[tex]\angle B=\angle C=x\ (say)[/tex]........Base angles are equal
Also we have,
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\46+x+x=180\\\therefore 2x =180-46=134\\\therefore x=\dfrac{134}{2}=67\°[/tex]
Therefore, the measure of an acute base angle of the trapezoid are
[tex]\angle A=\angle B=67\°[/tex]
