Find the value of x.
m<2 = 2x + 20

The answer to your question is x = 11

Step-by-step explanation:

Data

m∠2 = 2x + 20

x = ?

Exterior angle = 114°

Process

1.- Find the interior angle (it will be y)

    180° = 114 + y

    y = 180 - 114

    y = 66°

2.- These are Isosceles triangles because two of their sides measure the same.

- Find the different angle

       180 = 66 + 66 + z

       z = 180 - 66 - 66

       z = 48°

- Angle z and angle a are complementary angles

        z + a = 90

        a = 90 - 48

        a = 42°

- Angle a and angle 2 measure the same

        a = 2 = 42°

3.- Find x

             2x + 20 = 42

- Solve for x

             2x = 42 - 20

             2x = 22

               x = 22/2

               x = 11        

x = 11

Step-by-step explanation:

NOTES: Congruent sides mean congruent angles

              Linear Pair = 180°

              Triangle Sum Theorem means sum of all 3 angles = 180

              Right angle = 90°, so complimentary angles = 90°

Bottom Triangle:

Use Linear Pair to discover that 114° + 66° = 180°

Use Congruent sides to show that the other base angle = 66°

Use Triangle Sum Theorem to show that the vertex angle = 48°

      66° + 66° + vertex angle = 180°   →   vertex angle = 48°

Top Triangle:

Use congruent sides to show that the other base angle = <2

Complimentary Angles = 90°:

<2 from top triangle and 48° from bottom triangle are complimentary

See attachment for calculation that x = 11

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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