Question

(20 POINTS) One side of a trapezoid is extended and the dotted line forms a right angle with the extended line.

Answer 1

Answer:

C

Step-by-step explanation:

A and B are out because we can already tell that 65 and 75 are smaller than the 90 degrees whichs this angle is even higher than.If you see or use a protrater you can see it seems more likely to 115 because 155 would be much more open.

Answer 2

Answer: p = 115* (degrees)

Explanation:

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.

Process:

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

Answer: p = 115*

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*