Question

Finding the measure of angles

Answer 1

A = 72

B = 108

C = 30

Explanation:

Triangle properties

In order to find the measures of the angles it's important that we highlight the following properties.

1. The sum of the angles in a triangle is 180 degrees
2. Angles on a straight line (supplementary angles) add up to 180 degrees

Using these properties we can easily find the measures of the angles

Finding A

In the triangle on the left, we are already given two angles and we want to find A. By using the first property we know that the sum of the angles must add to 180 degrees

This means that, 46° + 62° + A = 180°

46° + 62° + A = 180°

==> combine like terms

108° + A = 180°

==> subtract 108 from both sides

A = 72°

Finding B

Now that we have found the measure of A, we can find the measure of B by using the second property. Because the two angles are formed on a straight line we know that A + B = 180°

If A = 72°, Then 72° + B = 180

72° + B = 180

==> subtract 72 from both sides

B = 108°

Finding C

Now that we found the value of B we can use the first property to find C.

If the angle measures of a triangle add up to 180 degrees, then C + B + 42° = 180°

If, B = 108° , then C + 108° + 42° = 180

C + 108° + 42° = 180

==> combine like terms

C + 150 = 180

==> subtract 150 from both sides

C = 30