Question

Behind my math class help pls

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Part a)

Given that the two parallel lines are crossed by a transversal line.

Given that

m∠2 = 2x + 54 and m∠6 = 6x - 11

Angle ∠2 and ∠6 are corresponding angles.

Corresponding angles are congruent.

Thus,

m∠2 = m∠6

2x + 54 = 6x - 11

flipe the equation

6x - 11 = 2x + 54

subtract 2x from both sides

6x - 2x - 11 = 2x - 2x + 54

4x - 11 = 54

adding 11 to both sides

4x - 11 + 11 = 54 + 11

4x = 65

dvide both sides by 4

4x/4 = 65/4

x = 16.2500    (round to 4 decimal places)

Part b)

We have already determined

x = 16.2500

Given

m∠2 = 2x + 54

substitute x = 16.2500 in the euation

        = 2(16.2500) + 54

        = 86.5°

As angle ∠2 and angle ∠1 lie on a straight line. Hence, the sum of their angles must be 180°.

i.e.

m∠1 + m∠2 = 180°

substituting m∠2 =  86.5° in the equation

m∠1 + 86.5°  = 180°

subtracting 86.5° from both sides

m∠1 + 86.5° - 86.5° = 180° - 86.5°

m∠1 = 93.5°

Therefore, the measure of angle m∠1 is:

• m∠1 = 93.5°