Answer:
∠T = 67.5
∠V = 22.5
Step-by-step explanation:
Angles of a triangle rule: The angles of a triangle should add up to equal 180
That being said we create an equation to solve for x
180 = 3x + x + 90 ( there is a right angle indicated by the square at the bottom right of the triangle. A right angle has a measure of 90 degrees so that is where the 90 cam from )
Now that we've created an equation we want to solve for x
180 = 3x + x + 90
step 1 combine like terms
3x + x = 4x
now we have 180 = 4x + 90
step 2 subtract 90 from each side
180 - 90 = 90
now we have 90 = 4x
step 3 divide each side by 4
4x / 4 = x
90 / 4 = 22.5
we're left with x = 22.5
Now we want to find ∠T and ∠V
To do so we replace x in the given expressions with 22.5
for ∠V
∠V = x so ∠V = 22.5
for ∠T
∠T = 3x
* replace x with 22.5 *
3 (22.5) = 67.5
Hence ∠T = 67.5
Answer: ( -7 , -3 )
Step by step:
The point: ( X , Y )
Left 2 units = change X by -2
So, -5 subtract by 2 equals -7
Down 3 units = change Y by -3
So, 0 subtract by 3 equals -3
Now, X = -7 and Y = -3, so the answer is ( -7 , -3 )
Hope this helps! Please tell me if I did anything wrong, thank you!
Answer: Choice C
x/w and z/(y+v)
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Explanation:
All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.
Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).
So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w
x/w is one of the answers
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Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z
Therefore,
sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)
z/(y+v) is the other answer
Side note: triangle ACD is not used at all.
