Answer:
D. 108 degrees
Step-by-step explanation:
use the formula (n-2)180/n, n being number of sides.
In this case, the number of sides is 5.
plug it into the formula and solve:
(5-2)180/5
(3)180/5
540/5
108 degrees.
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Answer:
Part 1)
Part 2) The height of the pole is
Step-by-step explanation:
Let
x------> the length of the pole
y------> the length of the shadow
we know that
-----> equation A
Applying the Pythagoras Theorem to find the distance (hypotenuse in a right triangle)
-----> equation B
substitute equation A in equation B and solve for x
squared both sides
-----> equation that represent the situation
solve for x