Answer:
Problem 13:
Again, use the Triangle Angle Sum theorem but also use the Vertical Angles Theorem. The Vertical Angles theorem states that when two lines intersect, vertical angles are congruent.
First, find the missing x value of the bigger triangle.
57 + 43 + x = 180
100 + x = 180
100 - 100 + x= 180 - 100
x= 80
Now that we know the missing value of the bigger triangle (80) then we can concluded that the other missing value of smaller triangle is ALSO 80˚ by the Vertical Angles theorem.
To find the two x values, write the equation that models Triangle Angle Sum theorem.
80 + x + x = 180
Simplify
80 + 2x = 180
Subtract 80 by both sides.
80 - 80 + 2x = 180 - 80
2x= 100
Divide both sides by 2.
2x/2 = 100/2
x= 50
Therefore, the two x values are 50˚
Problem 14:
In this problem, they try to confuse/ trick you. Dont' worry, just follow the same principles as above. To find the missing value of x, you first need to find the the missing angle of the right triangle. To do this, make the equation:
65 + 90 + x = 180
155 + x = 180
155 - 155 + x = 180 - 155
x= 25
This value of x is the answer, however, you can also add 25 to the 80˚ angle of the other triangle to find the full value of that corner angle (Since the two triangles split that angle in half)
80 + 25 = 105
Now to find x, make the equation:
105 + 50 + x = 180
155 + x = 180
155 - 155 + x = 180 - 155
x= 25.
As you see, there are two ways to solve and view this problem.
