The isosceles trapezoid is part of an
isosceles triangle with a 46° vertex angle.
enter the measure of an acute base angle of
the trapezoid.

Therefore, the measure of an acute base angle of  the trapezoid are

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

........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°.

Therefore, the measure of an acute base angle of  the trapezoid are

Reason 4: Vertical Angles

Step-by-step explanation:

Vertical angles (aka Vertically opposite angles are angles that are opposite each other, separated by a straight "cross" line)

This is a question on geometry + angle properties / congruence and similarity. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)