I believe the answer is A.
Answer:
The answer is below
Step-by-step explanation:
∠EFG and ∠GFH are a linear pair, m∠EFG = 3n+ 21, and m∠GFH = 2n + 34. What are m∠EFG and m∠GFH?
Solution:
Two angles are said to form a linear pair if they share a base. Linear pair angles are adjacent angles formed along a line as a result of the intersection of two lines. Linear pairs are always supplementary (that is they add up to 180°).
m∠EFG = 3n + 21, m∠GFH = 2n + 34. Both angles form linear pairs, hence:
m∠EFG + m∠GFH = 180°
3n + 21 + (2n + 34) = 180
3n + 2n + 21 + 34 = 180
5n + 55 = 180
5n = 125
n = 25
Therefore, m∠EFG = 3(25) + 21 = 96°, m∠GFH = 2(25) + 34 = 84°
I will show you how to do the first one.....we are finding the GCF...the largest number that goes into each number (same for variables)
1.) 20yx , 80x³ ( factor each number and variable)
20 = 2, 4, 5, 10, 20
y = y
x = x
80 = 2, 4, 5, 8, 10, 16, 20, 40, 80
x³ = x, x, x
what is the largest number that 20 and 80 have in common? 20...
how about the variables? x
so, the Greatest Common Factor (GCF is 20x)
∠LQK+∠GQL=90º
Therefore:
(4n-15)+(3n)=90
7n=90+15
7n=105
n=105/7
n=15
∠LQK=4n-15=4(15)-15=60-15=45
Answer: ∠LQK=45º
Answer:
Step-by-step explanation:
If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...
Anyways, the half angle identity for tangent is
There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.
If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:
which simplifies a bit to
and a bit more to
Bring up the lower fraction and flip it to divide to get
which of course simplifies to
-3. Choice A.
