Answer:
x = 65°
Step-by-step explanation:
these are vertical angles, which are congruent
145 = 2x + 15
130 = 2x
65 = x
Consecutive angles in a paralleogram have sum 180




And
- 7y+3+86=180
- 7y+89=180
- 7y=91
- y=13
And
opposite angles are equal
According to the Alternate Exterior Angles Theorem if a pair of Parallel lines are intersected by a transversal(t) then the alternate exterior angle are congurent.-<u>Alternate Exterior Angles theorem and Linear Pair theorem</u>
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Step-by-step explanation:
Alternate exterior angles are said to be those angles that are outside the "block" which is formed by the parallel lines and are placed on the opposite sides of the transversal(t)
From the question we can say that both ∠2 and ∠7 are outside the parallel lines and ∠2 is on the right side of the transversal (t) and ∠7 is on the left side of the transversal. <u>This makes ∠2 and ∠7 alternate exterior angles.</u>
<u>A linear pair is referred to as a pair of angles that are formed from a straight line. When ∠7 and ∠8 combined together they form a straight line this makes them a linear pair.</u>
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<u>According to the Alternate Exterior Angles Theorem if a pair of Parallel lines are intersected by a transversal(t) then the alternate exterior angle are congurent. Hence both Alternate Exterior Angles theorem and Linear Pair theorem is applicable</u>
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Answer:
a) The maximum height is approx 15.5 unit.
b) The time it will take for Joey to reach the water is 1.45 hour.
Step-by-step explanation:
Given : When Joey dives off a diving board, the equation of his pathway can be modeled by 
To find : a) Find Joey's maximum height.
b) Find the time it will take for Joey to reach the water.
Solution :
Modeled
....(1)
a) To find maximum height
Derivate (1) w.r.t. t,

For critical point put h'=0,



Derivate again w.r.t. t,

It is maximum at t=0.46875.
Substitute t in equation (1),



The maximum height is approx 15.5 unit.
b) To find the time it will take for Joey to reach the water.
Put h=0 in equation (1),
Apply quadratic formula, 
Here, a=-16 , b=15, c=12
Reject negative value.
The time is t=1.45.
The time it will take for Joey to reach the water is 1.45 hour.