9. x = 60
10. C. 180
11. equal
12. 2p + 2
Step-by-step explanation:
9.
Name the angle C2 = 120
Name the three interior angles of the triangle:
+) Angle A = x + 5
+) Angle B = x - 5
+) Angle C1 is the last one
As it can be seen, angle C2 and angle C1 are supplementary angles.
=) ∠ Angle C1 + ∠ Angle C2 = 180
=> ∠ Angle C1 + 120 = 180
=> ∠ Angle C1 = 180 - 120 = 60
As ABC is a triangle, total measure of three interior angles are 180 degree
=> Angle A + Angle B + Angle C1 = 180
=> x + 5 + x - 5 + 60 = 180
=> 2x = 180 - 60 -5 + 5 = 120
=> x = 120/ 2= 60
x = 60
10.
According to the triangle exterior angle theorem, the exterior angle of a triangle and its adjacent interior triangle are two supplementary angles.
Total measure of two supplementary angles are 180 degree. (Exterior angle of the triangle + Its adjacent interior angle = 180 degree)
=> The total measure of an exterior angle of a triangle and its adjacent interior angle add to 180 degree.
=> Answer C: 180 degree
The measure of an exterior angle of a triangle is equal to the total measure of the two opposite interior angles.
In a triangle, total measure of three interior angles (includes: two opposite interiors and one adjacent angle) are 180 degree.
=> Two opposite interior angles + Adjacent interior angle = 180 degree
=> Exterior angle of the triangle + Its adjacent interior angle = 180 degree
11.
According to the triangle external angle theorem, the exterior angle of a triangle and its adjacent interior triangle are two supplementary angles.
Total measure of two supplementary angles are 180 degree.
=> Exterior angle of the triangle + Its adjacent interior angle = 180 degree
In a triangle, total measure of three interior angles (includes: two remote interiors and one adjacent angle) are 180 degree.
=> Two remote interior angles + Adjacent interior angle = 180 degree
=> Two remote interior angles + Exterior angle of the triangle = 180 degree
So that the measure of an exterior angle of a triangle and the sum of the measures of the two remote interior angles are equal.
12.
p is the number of math problems that Hayden has completed.
The number of math problems Jamie completed was 2 more than twice the number that Hayden completed.
Twice the number of math problems Hayden completed was: 2p
=> Two more than twice the number of math problems Hayden completed was: 2p + 2
=> Number of math problems Jamie completed was: 2p + 2
Equation: 2p + 2
The total math problems Hayden and Jamie completed were 20.
=> The number of math problems Hayden completed + the number of math problems Jamie completed = 20
=> p + (2 + 2p) = 20
=> 3p + 2 = 20
=> 3p = 20 - 2 = 18
=> p = 18/3 = 6
