Answer:
angle 1 = 124
angle 2 = 56
angle 3 = 124
angle 4 = 56
Step-by-step explanation:
This problem is a bit like a puzzle. To make notation easier I'm going to do this:
angle 1 = a
angle 2 = b
angle 3 = c
angle 4 = d
Now, let's start with what we know from the image.
All angles added together form a circle or 360 degrees
a + b + c + d = 360
In the same regard a + d = 180, and b + c = 180
Also,
a = c
and
b = d
It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.
d = 1/4(a) + 25
If we look at all the equations we have, we can see that two of the equations have two of the same variables:
a + d = 180
and
d = 1/4(a) + 25
Using substitution we can take the second equation substitute it for d in the first equation giving us:
a + (1/4(a) + 25) = 180
Now we just solve for a
[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]
Therefore a, or angle 1, is 124
Since a = c, then c, or angle 3, is also 124
Since a + d = 180 and a = 124 then
d = 180 -124
d = 56
So, d, or angle 4, is 56
And because b = d then b, or angle 2, is also 56
a = 124
b = 56
c = 124
d = 56
For extra measure, we can check our work by using the first equation
a + b + c + d = 360
124 + 56 + 124 + 56 = 360
