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 =
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.