Calculate 7 Angles with Parallel Lines: Given Angle 115°

Question

a is parallel to b.

Calculate the angles shown in the diagram.

00:00 Find the angles

00:03 Adjacent angles are supplementary to 180

00:07 Therefore subtract the known angle from 180 to get the angle

00:14 *

00:28 (2,115) Vertical angles are equal

00:32 (3,60) Also a pair of vertical angles

00:48 (4,115) Corresponding angles between parallel lines are equal

00:55 (6,4) Vertical angles are equal

01:03 (5,65) Corresponding angles between parallel lines are equal

01:11 (5,7) Vertical angles are equal

01:14 And this is the solution to the question

Given that according to the definition, the vertex angles are equal to each other, it can be argued that:

$115=2$ Now we can calculate the second pair of vertex angles in the same circle:

$1=3$

Since the sum of a plane angle is 180 degrees, angle 1 and angle 3 are complementary to 180 degrees and equal to 65 degrees.

We now notice that between the parallel lines there are corresponding and equal angles, and they are:

$115=4$

Since angle 4 is opposite to angle 6, it is equal to it and also equal to 65 degrees.

Another pair of alternate angles are angle 1 and angle 5.

We have proven that: $1=3=65$

Therefore, angle 5 is also equal to 65 degrees.

Since angle 7 is opposite to angle 5, it is equal to it and also equal to 115 degrees.

That is:

$115=2=4=6$

$65=1=3=5=7$

1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°