Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
So basically, the first question after the word problem is asking you to write an equation to represent the value of Mama's car after a certain amount of years (t). Since the value of her car decreases by 3% each year, you could multiply 3% by the original value of her car, to find what 3% is, OR you could subtract 19,400 (the value of her car after 1 year) from 20,000 INSTEAD of multiplying 20,000 by 3%.
Equation: value=20,000 - 600t
To answer the next question, just plug it into the equation you created.
500<20,000 - 600t
-19500< -600t
32.5>t
Final Answer: It would take at least 32 and 1/2 years for the value of Mama's car to be less than $500.
Hope this helps!! :)
Answer:
1. 30
2. 150
Step-by-step explanation:
Lets assume tan(x) = u
Now we solve for 'u'
add 1 on both sides
, divide both sides by 3
Take square root on both sides
We replace tan(x) for 'u'
x = 30 because 
in first quadrant
x = 30 (tan is positive in first quadrant)
x = 150 because 
in second quadrant
tan is negative in second quadrant
