This is due in 15 minutes
all 3 !

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

Step-by-step 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