Calculate the Missing Angle B in Triangle ABC: Given 105° and 45°

Question

According to the data in the diagram, calculate a size of angle ABC.

00:00 Find angle ABC

00:05 Vertical angles are equal

00:15 The sum of angles in a triangle equals 180

00:21 Let's group terms and isolate ABC

00:48 And this is the solution to the question

Note that from the diagram we are able to determine the value of angle BAC, since its corresponding angle is equal to 105.

Now in the triangle we are given two angles:

$BAC=105$

$BCA=45$

Since the sum of angles in a triangle is equal to 180, we can calculate angle ABC:

$180-105-45=30$