Answers for pictures 1, 2, &3
Question 1: P = 35 degrees
It is given to us that angles N and P are complementary.
Complementary angles means the sum of the angles = 90 degrees.
Because angles N and M are supplementary, meaning they = 180 degrees, you can subtract angle M from 180.
180 - M = N
180 - 125 = 55
N = 55 degrees
Now that we know N = 55 degrees, we subtract that from 90 degrees to find P for N + P = 90 degrees, so if we subtract 55 from 90 we will get the value of angle P.
90 - N = P
90 - 55 = 35
P = 35 degrees!
Question 2: Option 4
We are trying to figure out which angles are congruent to one another.
We can rule out option one, for angles 1 & 4 are supplementary meaning their sum = 180 degrees.
The same applies for options 2 & 3, leaving us with the correct answer, option 4. We can make sure this is true because angles 3 & 5 are alternate interior angles, and alternate interior angles of parallel lines are congruent.
Question 3: x = 5
The three different angles add up to 180 because they are a straight angle.
First, we need to find out what 9 and 10 are equal to.
To do so, we can subtract 85 from 180.
180 - 85 = 9x + 10x
9x + 10x = 95
Now that we have an equation, we can simplify to find the value of x.
9x + 10 = 95
19x = 95
Divide by 19 on each side to isolate the variable x
x = 5
Hope this helps!