# Question Video: Determining Which Inequality Applies to the Internal and External Angles of a Triangle Mathematics

Which of the following inequalities is correct? [A] πβ π΄π΅πΆ < πβ π΅π΄πΆ < πβ π΄πΆπ΅ [B] πβ π΄π΅πΆ > πβ π΅π΄πΆ > πβ π΄πΆπ΅ [C] πβ π΅π΄πΆ > πβ π΄π΅πΆ > πβ π΄πΆπ΅ [D] πβ π΅π΄πΆ < πβ π΄π΅πΆ < πβ π΄πΆπ΅ [E] πβ π΄πΆπ΅ < πβ π΄π΅πΆ < πβ π΅π΄πΆ

02:05

### Video Transcript

Which of the following inequalities is correct? (A) The measure of angle π΄π΅πΆ is less than the measure of angle π΅π΄πΆ is less than the measure of angle π΄πΆπ΅. Or (B) the measure of angle π΄π΅πΆ is greater than that of angle π΅π΄πΆ which is greater than the measure of angle π΄πΆπ΅. (C) The measure of angle π΅π΄πΆ is greater than that of π΄π΅πΆ which is greater than that of π΄πΆπ΅. Or option (D), the measure of angle π΅π΄πΆ is less than the measure of angle π΄π΅πΆ is less than that of π΄πΆπ΅. Or finally, the measure of angle π΄πΆπ΅ is less than the measure of angle π΄π΅πΆ which is less than the measure of angle π΅π΄πΆ.

We note that each of the five options involves the measures of the three angles π΄π΅πΆ, π΅π΄πΆ, and π΄πΆπ΅ and that weβre given the measure of one of these. Thatβs angle π΄πΆπ΅, which is 29 degrees. And so to answer the question, we need to find the measures of the two interior angles π΅π΄πΆ and π΄π΅πΆ.

We can find the measure of angle π΅π΄πΆ by noting that the measures of the angles that make a straight line sum to 180 degrees. And so we have 109 degrees plus the measure of angle π΅π΄πΆ equals 180 degrees. Subtracting 109 degrees from both sides gives us the measure of angle π΅π΄πΆ equals 71 degrees. Next, we can find the measure of angle π΄π΅πΆ by recalling that the measure of the interior angles of a triangle sum to 180 degrees. Thus, we have 71 degrees plus the measure of angle π΄π΅πΆ plus 29 degrees equals 180 degrees.

Now, subtracting 71 and 29 degrees from both sides, we have the measure of angle π΄π΅πΆ equals 80 degrees. Since 80 is greater than 71, which in turn is greater than 29, we see that the measure of angle π΄π΅πΆ is greater than the measure of angle π΅π΄πΆ which is greater than the measure of angle π΄πΆπ΅. And this corresponds to option (B), so option (B) is correct.