Answer:
m<1 = 51 degrees
m<2 = 18 degrees
m<3 = 123 degrees
m<4 = 39 degrees
Step-by-step explanation:
To solve this problem, let's first try to find the measure of angle 1.
To do this, we must remember that the sum of the interior angles of a triangle must equal 180 degrees. Using this knowledge, we can set up the following equation:
72 + 57 + m<1 = 180
Our first step in solving this equation is to simplify the left side by adding together the two constant terms.
129 + m<1 = 180
Next, we can subtract 129 from both sides of the equation.
m<1 = 51 degrees
Now, we can solve for angle 2.
We can see that angle 2 and the angle measuring 72 degrees together make a right angle, which is 90 degrees. From this observation, we can set up the following equation:
m<2 + 72 = 90
To solve, we subtract 72 from both sides of the equation.
m<2 = 18 degrees
Now, we can solve for angle 3.
We can see from the diagram that angle 3 and the angle measuring 57 degrees are supplementary. This means that their sum should equal 180 degrees, and the two angles together make a straight line. This lets us set up the following equation:
m<3 + 57 = 180
To solve, we subtract 57 from both sides of the equation.
m<3 = 123 degrees
Finally, we can solve for angle 4.
We can solve for angle 4 using the same strategy we used to solve for angle 1. Our equation for angle 4 is as follows:
m<2 + m<3 + m<4 = 180
18 + 123 + m<4 = 180
Let's first simplify the left side of the equation.
141 + m<4 = 180
We can subtract 141 from both sides of the equation as our next step.
m<4 = 39 degrees
Therefore, the correct answers are m<1 = 51 degrees, m<2 = 18 degrees, m<3 = 123 degrees, and m<4 = 39 degrees.
Hope this helps!
