Answer:
Part 1) The measure of the exterior angle is 128°
Part 2) The measure of angle x is 30°
part 3) The value of x is 25 units
Explanation:
Part 1)
step 1
Find the measure of the third internal angle of the triangle
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
Let
c----> the measure of the third internal angle
42+(9x-4)°+c°=180°
c=180°-42°-9x+4°
c=142°-9x
step 2
Find the value of x
we know that
c+(12x+8)°=180° ----> by supplementary angles
substitute
142°-9x+(12x+8)°=180°
3x=30°
x=10°
step 3
Find the measure of the exterior angle
(12x+8)°=(12(10)+8)°=128°
Part 2) Find the value of x
The figure show a equilateral triangle ( has three equal internal angles and three equal sides) and an isosceles triangle ( has two equal internal angles and two equal sides)
Remember that
The internal angles of a equilateral triangle is 60 degrees
so
The vertex angle of the isosceles triangle is equal to
180°-60°=120° ----> by supplementary angles
therefore
The base angle of the isosceles triangle is equal to
2x+120°=180°
2x=60°
x=30°
Part 3) we know that
if AB is a midsegment
then
(4x-10)/2=45
solve for x
4x-10=90
4x=100
x=25 units