Answer: p = 115* (degrees)
<h3>Explanation:</h3>
What we know:
- The trapezoid forms a right triangle
- The right triangle has the angles 25*, 90*, and an unknown
- The internal angles of a triangle add up to 180*
- The unknown value p is a supplementary angle to the right triangle's unknown angle
How to solve:
By finding the degree of the 3rd angle in the right triangle, we can use the rules of supplementary angles to find the value of p.
We will use D to represent the total amount of degrees, which will equal 180*. X will represent an unknown angle. An asterisk represents the degree symbol.
<h3>Process:</h3>
Missing right triangle angle
Set up equation D = 25 + 90 + x
Substitute 180 = 25 + 90 + x
Simplify 180 = 115 + x
Isolate variable -115 -115
Solution 65* = x
Value of p using supplementary angles
Set up equation D = x + p
Substitute 180 = 65 + p
Isolate variable -65 -65
Solution 115* = p
<h3>Answer: p = 115*</h3>
Check:
We can do a check based on estimation. Assuming that the trapezoid and triangle form a box with all 90* corners and that p = 115*, then adding p and all of the other trapezoid angles should result in 360*
Firstly, we need the values of these 4 angles.
The first angle, labeled p, should be 115*. If our equation is untrue, then this value will fail the check.
The second angle will be the one at the bottom-left, which is 90* according to our box statement.
The third angle is the one located at the bottom-right, which is also 90* from the box statement.
The fourth angle is not 90* or 115*, but we can solve its value.
Because we have stated that the right triangle and trapezoid form a box with 4 90* corners, the sum of the fourth angle and the 25* from the right triangle must form a right angle. Let's find the value:
D = 25 + x
90 = 25 + x
(90 = 25 + x) - 25
65* = x
Therefore, the fourth angle has 65*
Now, adding the degrees from all 4 angles should result in a total of 360*. If it does, then our value of p = 115* will pass the check.
D = 90 + 90 + p + x
360 = 90 +90 + 115 + 65
360 = 180 + 180
360 = 360
Therefore, p = 115*
