Question

PLZ HELP ASAP!!

the exterior sides of two adjacent angles make a right angle. the first angle has a measure that is six more than half the second. what are the measures of both angles

Answer 1

34 and 56

Explanation:

I took the quiz and got it right.

Answer 2

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"

`\text{ first angle } = 6 + (x)/(2)`

Since these two angles forms 90 degrees,

first angle + second angle = 90

`x + 6 + (x)/(2) = 90\\\\(2x + 12 + x)/(2) = 90\\\\2x + 12+x = 180\\\\3x + 12 = 180\\\\3x = 180 - 12\\\\3x = 168\\\\x = 56`

Therefore, first angle is:

`\rightarrow 6 + (56)/(2) = 6 + 28 = 34`

Thus measure of first angle is 34 degrees and measure of second angle is 56 degrees