Question

Lines c and d are parallel. Parallel lines c and d are cut by transversals s and t. Clockwise from top left, the angles formed by c and t are blank, blank, 1, blank; formed by c and s are blank, blank, blank, 2; formed by s, t, and d are blank, 3, (5 x minus 1) degrees, (2 x + 10) degrees, 87 degrees, blank. Which statements about the relationships between the angle measures are true? Check all that apply. Measure of angle 1 = (2 x + 10) degrees Measure of angle 3 = 87 degrees Measure of angle 2 = (2 x + 10 + 5 x minus 1) degrees Measure of angle 1 + measure of angle 2 = measure of angle 3 87 + 2 x + 10 + 5 x minus 1 = 180
Please help ASAP!

Answer 1

Answer:

Options (1), (2) and (5) are true.

Step-by-step explanation:

Option (1). m∠1 = (2x + 10)°

lines c and d are the parallel lines and t is a transverse.

Therefore, m∠1 = (2x + 10)° [corresponding angles]

This option is true.

Option (2). m∠3 = 87°

Since ∠3 and angle having measure equal to 87° are the vertical angles therefore, both the angles will be equal in measure.

This option is true.

Option (3). m∠2 = (2x + 10 + 5x - 1)°

m∠2 = (5x - 1)° [Since both the angles are interior alternate angles]

Therefore, this option is not true.  

Option (4). m∠1 + m∠2 = m∠3

(5x - 1) + (2x + 10) + 87 = 180° [Sum of liner angles at a point is 180°]

7x + 96 = 180

7x = 180 - 96

x = $\frac{84}{7}$

x = 12

Therefore, m∠1 = (2x + 10) = 34°

                 m∠2 = (5x - 1) = 59°

                 m∠3 = 87°

For the given relation,

m∠1 + m∠2 = m∠3

34 + 59 = 87

93 = 87

Not true.

Therefore, this option is not correct.

Option (5). 87 + 2x + 10 + 5x - 1 = 180°

True.

Since these angles are the linear angles so the sum of all angles = 180°

Therefore, the given option is correct.

Options (1), (2) and (5) are the true.