Question

Find the value of x.
m<2 = 2x + 20​

Answer 1

Answer: x = 11

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

Answer 2

The answer to your question is x = 11

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