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

Question

Look at the diagram below.

Calculate the size of angle ABC.

00:00 Calculate angle ABC

00:05 Lines are parallel according to the given data

00:12 Alternate angles are equal between parallel lines

00:27 Lines are parallel according to the given data

00:35 Corresponding angles sum to 180 between parallel lines

00:48 We'll substitute appropriate values according to the given data and solve for the angle

00:55 Let's isolate angle HBC

01:05 This is angle HBC

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

01:17 And this is the solution to the problem

In the drawing before us, we can see three parallel lines and two lines that intersect them.

We are asked to find 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.

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 to find angle ABC

$ABH + CBH = ABC$

$92 + 49 = 141$

$141$