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 …

Question

asked Jul 5, 2021 96.7k views

2 Answers

RoundPi · Answer 1 · 2021-07-09T05:01:22+0000

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