Angles in Parallel Lines: Using additional geometric shapes

Look at the following parallelogram.

Calculates the size of the angle $∢\text{ABC}$.

Since we are dealing with parallels, we have 2 pairs of parallel lines.

As a result, we can argue that angle ADB and angle DBC are alternate angles between parallel lines, therefore both are equal to each other at 44 degrees:

$ADB=DBC=44$

Now we can calculate angle ABC:

$ABC=ABD+DBC$

Let's substitute the known values:

$ABC=40+44=84$

84

Look at the parallelogram of the figure below.

What are the angles in the parallelogram?

Cannot be solved.

A parallelogram is shown below.

a is parallel to b.

Calculate the size of the highlighted angle.

87

The trapezoid ABCD is isosceles.

AD = AE

Calculate angle $\alpha$.

A,B=110.5 | C,D=69.5 | $\alpha=110.5$

Look at the polygon in the diagram.

Which lines are parallel to each other?

d,a

Given the rectangle find a X

32

Given the trapezoid, find a X

83

ABCD is a parallelogram.

The highlighted part of the circle is $\frac{2}{5}$ of its circumference.

Calculate the angle DCE and the value of X.

36°, X=42.33

Look at the parallelogram below.

The labelled angles are acute.

For what values of X is there a solution?

No solution.

In the drawing, a rectangle and a circle whose center is the corner of the rectangle.

Given R=4

What is the length of the highlighted part in the drawing?

$\frac{32}{45}\pi$

Below is the trapezoid ABCD.

Given that D is the center of the circle and the highlighted part constitutes $\frac{1}{6}$ of the circumference,

what type of trapezoid is it?

Isosceles