Question Video: Finding the Measure of an Interior Angle of a Triangle | Nagwa Question Video: Finding the Measure of an Interior Angle of a Triangle | Nagwa

# Question Video: Finding the Measure of an Interior Angle of a Triangle Mathematics • First Year of Preparatory School

## Join Nagwa Classes

Find the measure of β π΄πΆπ΅.

02:20

### Video Transcript

Find the measure of angle π΄πΆπ΅.

Letβs have a closer look at the figure weβve been given. There is a triangle formed by connecting the points π΄, π΅, and πΆ. The measure of one of the interior angles in this triangle, angle π΄π΅πΆ, has been marked as 35 degrees. And the measure of the angle weβve been asked to calculate, angle π΄πΆπ΅, has been marked as π₯. Weβre also given the measure of an angle outside the triangle, which is 65 degrees. The final thing to note is that line π΅π΄ and line πΆπ·, as weβve now labeled it, are parallel, as indicated by the arrows along their lengths.

Now, we need to consider how we can use all this information to determine the measure of angle π΄πΆπ΅. Because lines π΅π΄ and πΆπ· are parallel, angle π΄πΆπ· and angle πΆπ΄π΅ are alternate angles. Alternate angles are of equal measure, so this tells us that the measure of angle πΆπ΄π΅ is also 65 degrees.

We now know the measures of two of the interior angles in triangle π΄π΅πΆ, and we wish to calculate the measure of the third. We can recall that the sum of the measures of the interior angles in any triangle is 180 degrees. We can therefore form an equation using the measures of the interior angles of triangle π΄π΅πΆ. π₯ plus 35 degrees plus 65 degrees equals 180 degrees. This equation simplifies to π₯ plus 100 degrees equals 180 degrees. π₯ is therefore equal to 180 degrees minus 100 degrees, which is 80 degrees.

Remember π₯ represents the measure of angle π΄πΆπ΅. So using the sum of the measures of the interior angles in a triangle, we found that the measure of angle π΄πΆπ΅ is 80 degrees.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions