Answer:
15.
If we look at angle BOD, that would form a right angle (90°), given that one part of that whole angle is 30°, the other would be;
30° + x = 90°
-30 -30
x = 60°, therefore ∠BOC = 60°.
If we take a look at angle EOC, we can see that that angle is a straight angle (180°), we can also see that a right angle (90°) is a part of that angle alongside the angle we just previously found (60°). So all of those angles plus the unknown angle (AOE) which we will consider 'x' summed up would result in 180 degrees.
Now we set up the equation;
90° + 60° + x = 180°
150 + x = 180
-150 -150
x = 30°, therefore ∠AOE = 30°.
16.
The sum of the interior angles in a triangle will always equal 180°. (We can also confirm this using the formula (n - 2) x 180.)
Given two of the angles, we must add them and the unknown angle(D) which we will consider 'x' to make it result in 180°.
Now we set up the equation;
55° + 18° + x = 180°
73 + x = 180
-73 -73
x = 107°, therefore ∠EDF = 107°.
17.
To find angle P, we must first find the supplement of 34° because 34° and the angle beside forms a straight angle (180°).
Set up an equation;
34 + x = 180
-34 -34
x = 146°, now that we've found the supplement, we add this supplement with the other given angle (23°) because all three angles (unknown angle which we will consider x + 23 + 146) will equal 180°(sum of interior angles of triangle).
146° + 23° + x = 180°
169 + x = 180
-169 -169
x = 11°, therefore ∠QPR = 11°.
18.
Seeing that the bigger triangle has a 90° angle (indicated with a square), and two other equal angles(indicated with the two lines on both legs of the big triangle), we solve for those two missing equal angles in the bigger triangle which we will then use to solve for the smaller triangle's angle.
2x + 90° = 180°
-90 -90
2x = 90
/2 /2
x = 45°, so now we know the two angles in the bigger triangle excluding the right angle.
One of those equal angles is vertical to the smaller triangle, and vertical angles are congruent.
Hence, the angle vertical to the bigger triangle in the smaller triangle will be 45°.
Now we solve for ∠CDE.
Add the two angles and the missing angle to equal 180°.
Set up the equation;
86° + 45° + x = 180°
131 + x = 180
-131 -131
x = 49°, so ∠CDE = 49°.
