What can we say about the third angle of the triangle?
True
Practice makes perfect
We are asked to determine whether the following statement is true or false.
If the sum of the measure of two acute angles of a triangle is greater than 90, then the triangle is acute.
Let's see what we can conclude about the third angle in a triangle, where the hypothesis is true. Let the acute angles of triangle △ ABC be ∠A and ∠B. The Triangle Angle-Sum Theorem gives a connection between the interior angle measures of a triangle.
Triangle Angle-Sum Theorem
The sum of the measures of the interior angles of a triangle is 180.
Let's rearrange this relationship to express one of the angle measures in terms of the other two.
Thus, if the sum of the measures of two acute angles in a triangle is greater than 90, then the third angle is acute.
This means that the triangle has three acute angles, so it is an acute triangle.
The statement is true.
