Problem 5
The missing interior angle of the triangle is also x because the base angles are congruent for any isosceles triangle. The triangle is isosceles because of the two tickmarks indicating those sides are the same length.
The angle 115 is supplementary to that angle x mentioned, so,
115+x = 180
x = 180-115
x = 65
Now to find y, we'll use the idea that adding the angles of any triangle always gets to 180
x+x+y = 180
65+65+y = 180
130+y = 180
y = 180-130
y = 50
--------------------
Answers: x = 65 and y = 50
=======================================================
Problem 6
We use the same idea as the previous problem. The missing angle is x because it's a congruent base angle. This missing angle x is supplementary to the 135 degree angle
x+135 = 180
x = 180-135
x = 45
Now add up the interior angles of the triangle, set the sum equal to 180 and solve for x
x+x+y = 180
45+45+y = 180
90+y = 180
y = 180-90
y = 90
--------------------
Answers: x = 45 and y = 90
=======================================================
Problem 8
This triangle is equilateral since all sides are the same length. Consequently, all angles are the same measure and equal to 180/3 = 60 degrees each.
Setting the bottom left angle equal to 60 and solving leads to
3y = 60
y = 60/3
y = 20
Do the same for the bottom right angle
2x = 60
x = 60/2
x = 30
--------------------
Answers: x = 30 and y = 20
=======================================================
Problem 9
The x and 110 degree angles are supplementary. They form a straight angle of 180 degrees
x+110 = 180
x = 180-110
x = 70
Focusing on the smaller right triangle on the right side, we have the upper acute angle x = 70, and the bottom acute angle y, and a right angle of 90 degrees.
These three angles must add to 180
x+90+y = 180
70+90+y = 180
160+y = 180
y = 180-160
y = 20
--------------------
Answers: x = 70 and y = 20
