Question

determine whether it is possible to draw a triangle with the given angle measures.
30°, 40°, 110°
if it is possible, which triangle drawn shows the angle measures given.
show hints
○ it is possible to draw a triangle with the given angle measures. the triangle looks like this.
○ it is possible to draw a triangle with the given angle measures. the triangle looks like this.
○ it is not possible to draw a triangle with the given angle measures.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate sum of given angles

Add the angles: \(30^\circ + 40^\circ + 110^\circ = 180^\circ\).

Step3: Analyze triangle types

Since the sum is \(180^\circ\), a triangle is possible. The angles include an obtuse angle (\(110^\circ\)), so it's an obtuse triangle (the top triangle with the obtuse angle). The bottom triangle looks equilateral/isosceles (all angles acute), so the first option's triangle (with the obtuse angle) matches.

Answer:

It is possible to draw a triangle with the given angle measures. The triangle looks like this. (The top - drawn triangle with the obtuse angle)