The measure of first angle is 34 degrees and measure of second angle is 56 degrees
Solution:
Given that, the exterior sides of two adjacent angles make a right angle
Therefore, these adjacent angles forms 90 degrees
Let the second angle be "x"
The first angle has a measure that is six more than half the second
Therefore,
first angle = 6 + half of "x"
[tex]\text{ first angle } = 6 + \frac{x}{2}[/tex]
Since these two angles forms 90 degrees,
first angle + second angle = 90
[tex]x + 6 + \frac{x}{2} = 90\\\\\frac{2x + 12 + x}{2} = 90\\\\2x + 12+x = 180\\\\3x + 12 = 180\\\\3x = 180 - 12\\\\3x = 168\\\\x = 56[/tex]
Therefore, first angle is:
[tex]\rightarrow 6 + \frac{56}{2} = 6 + 28 = 34[/tex]
Thus measure of first angle is 34 degrees and measure of second angle is 56 degrees
