Examples with solutions for Angles in Parallel Lines: Using additional geometric shapes

Exercise #1

Look at the following parallelogram.

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

AAABBBCCCDDD4044

Video Solution

Step-by-Step Solution

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 ADB=DBC=44

Now we can calculate angle ABC:

ABC=ABD+DBC ABC=ABD+DBC

Let's substitute the known values:

ABC=40+44=84 ABC=40+44=84

Answer

84

Exercise #2

A parallelogram is shown below.

a is parallel to b.

Calculate the size of the highlighted angle.

aaabbb12033

Video Solution

Answer

87

Exercise #3

Look at the parallelogram of the figure below.

What are the angles in the parallelogram?

81

Video Solution

Answer

Cannot be solved.

Exercise #4

Look at the polygon in the diagram.

Which lines are parallel to each other?

404040707070110110110150150150505050303030aaabbbcccdddeeefffggg

Video Solution

Answer

d,a

Exercise #5

The trapezoid ABCD is isosceles.

AD = AE

Calculate angle α \alpha .

7267ABCDE

Video Solution

Answer

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

Exercise #6

Given the rectangle find a X

84x26

Video Solution

Answer

32

Exercise #7

Given the trapezoid, find a X

104102120125x

Video Solution

Answer

83

Exercise #8

ABCD is a parallelogram.

The highlighted part of the circle is 25 \frac{2}{5} of its circumference.

Calculate the angle DCE and the value of X.

AAABBBCCCDDDEEE3X+17

Video Solution

Answer

36°, X=42.33

Exercise #9

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?

RRRDDDIII32

Video Solution

Answer

3245π \frac{32}{45}\pi

Exercise #10

Look at the parallelogram below.

The labelled angles are acute.

For what values of X is there a solution?

5x-42

Video Solution

Answer

No solution.

Exercise #11

Below is the trapezoid ABCD.

Given that D is the center of the circle and the highlighted part constitutes 16 \frac{1}{6} of the circumference,

what type of trapezoid is it?

AAABBBCCCDDDEEE30120

Video Solution

Answer

Isosceles