Help and definitions
First some definitions.
Adjacent angles share a common side. Imagine holding one page of a book up. The front cover and the page make one angle. The page and the back cover make a second angle that is ADJACENT to the first angle.
An acute angle is less than 90 degrees.
An obtuse angle is more than 90 degrees.
A right angle measures exactly 90 degrees.
A straight angle measures 180 degrees (and is really a straight line)
Complementary angles may or may not be adjacent but together they always add
up to 90 degrees.
Supplementary angles may or may not be adjacent but together they always add up to 180 degrees.
A linear pair is a pair of adjacent angles that are supplementary (which means together they form a straight line).
Angle 1 and angle 2 are linear pairs. Angle 2 measures 6 more than 5 times the measure of angle 1. How big is angle 2 and what is its type?
So angle 1 and 2 add to 180, because that's what linear pairs must do since the form a straight line.
Let angle 1 = x
angle 2 = 6 + 5x
x + 6 + 5x = 180
6 + 6x = 180
6x = 174
x = 29 (this is angle 1, but the question asked about angle 2)
Angle 2 = 6 + 5(29)
So angle 2 is 151 and is obtuse.
Does 151 + 29 equal 180? (Yes)
Is 151 six more than five times 29? (Yes)