Calculate Angle ABC: Using 92° and 131° in Parallel Lines Configuration

Question

Observe the diagram below.

Calculate the size of angle ABC.

00:00 Calculate angle ABC

00:05 The lines are parallel according to the given data

00:12 Alternate angles on parallel lines are equal

00:27 The lines are parallel according to the given data

00:35 The sum of the corresponding angles between the parallel lines is 180

00:48 Insert the appropriate values according to the given data and solve for the angle

00:55 Isolate angle HBC

01:05 This is angle HBC

01:12 The entire angle equals the sum of its parts

01:17 Here is the solution

In the given drawing we observe three parallel lines as well as two lines that intersect them.

We are asked to determine the size of angle ABC,

We can identify that the angle is actually composed of two angles, angle ABH and CBH.

In fact, we will calculate the size of each angle separately and combine them together.

Angle A is an alternate angle to angle ABH, and since alternate angles are equal, angle ABH equals 92.

Angle CBH is supplementary to angle DCB, supplementary angles equal 180, therefore we can calculate:

$HBC = 180-DCB$

$HBC = 180 - 131$

$HBC = 49$

Now that we have found angles ABH and CBH, we can add them together to find angle ABC

$ABH + CBH = ABC$

$92 + 49 = 141$

$141$