Answer:
72.32 degrees
Step-by-step explanation:
the picture shows a supplementary angle, which equals 180 degrees.
first, solve for x.
since the entire figure equals 180 degrees, set the equation equal to 180. then add in the measurements, which are 7x, 8x, and 44.4.
180 = 7x + 8x + 44.4
combine like terms (7x and 8x).
180 = 7x + 8x + 44.4 ⇒ 180 = 15x + 44.4
subtract 44.4 from both sides. the positive 44.4 will cancel out, so all you have to do is subtract 44.4 from 180.
180 - 44.4 = 135.6
now, your equation is...
135.6 = 15x
divide both sides by 15.
(135.6)/15 = (15x)/15 ⇒ 9.04 = x, <em>or</em> x = 9.04
now plug 9.04 in for x in both 7x and 8x.
7x ⇒ 7(9.04) ⇒ 63.28
<u>8</u><u>x</u><u> ⇒ 8</u><u>(9.04)</u><u> ⇒ </u><u>72.32</u>
<u></u>
<u><em>*the highlighted angle, 8x, is 72.32 degrees.</em></u>
checking your work:
now, all your measurements are 63.28, 72.32, and 44.4
check your work by adding all the measurements together and setting that equal to 180.
63.28 + 72.32 + 44.4 = 180
180 = 180
since both sides are equal, all of the values are correct!
now that you know your work is correct, it is fully safe to say that the highlighted angle is 72.32 degrees.
