Find the value of x.m<2= x + 85
2 answers:
<h3>Answer: x = -9</h3>
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Explanation:
Refer to the diagram below.
I've added the points A,B,C,D,E, and F to help set up the angles.
I've marked angle 2 as the variable y, which is angle DBA. I've also added in the variable w to help fill out triangle DBA. Those two remaining angles are congruent due to the congruent sides AB = DB. They are the base angles. Triangle DBA is isosceles.
Right next to angle DAB is angle CAB. These two angles combine to form the 90 degree angle. So that's where the 90-w comes from when setting up angle CAB. We have another isosceles triangle, so angles CAB and ACB are congruent.
Next, we can see that angles ACB and ECF are vertical angles. That makes them congruent and we can solve for w like so:
angle ACB = angle ECF
90 - w = 38
-w = 38-90
-w = -52
w = 52
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Now focus on triangle DBA again. The three angles add to 180, so,
w+y+w = 180
2w+y = 180
y = 180-2w
y = 180-2*52
y = 180-104
y = 76
This is the measure of angle 2. We have one more step left.
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Since we now know the measure of angle 2, we can use this to find x
angle 2 = 76 degrees
angle 2 = x+85
x+85 = 76
x = 76 - 85
x = -9
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Answer:
12√5
Step-by-step explanation:
According to the attached sketch, there are 2 triangles which we need to focus on, triangle A (in yellow) and triangle B (In red).
If you look at triangle A, we notice that X is the hypotenuse of triangle A. This means that X must be the largest length in triangle A, hence we can say that x must be greater than 24 (or 24 < x)
Now look at triangle B, in this case, they hypotenuse is 30 and x is the length of one of the sides. This means that x must be shorter than the hypotenuse (i.e x < 30)
from the 2 paragraphs above, we can see now that we can assemble an inequality in x
24 < x < 30
If we look at the choices, we can immediately ignore 33 because x must be less than 30,
working out the choices, we find that the only choice which falls into the range 24<x<30 is the 2nd choice 12√5 (= 26.83) (which is the answer)
The last 2 choices give values smaller than 24 and are hence cannot be the answer
