Final answer:
The measure of the angle is 155 degrees and there are three angles in total.
Step-by-step explanation:
In this problem, we are given that the measure of an angle is 5 more than six times its supplement. Let's denote the measure of the angle as 'x'. The supplement of the angle can be expressed as 180 - x. According to the given information, x = 6(180 - x) + 5.
We can rearrange the equation to solve for x: x = 1080 - 6x + 5 ==> 7x = 1085 ==> x = 155. Therefore, the measure of the angle is 155 degrees.
Since a triangle has three angles, there are three angles in total.