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An isosceles triangle has one angle with a measure greater than 100 degrees and another with a measure of x. which is true

The question has answer choices. Here they are..
a. x>80
b. x=80
c. x>40
d. x<40
e. x=40

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Ebenezer O. | Aerospace Engr & Air Traffic Control Grad For General Ed. TutoringAerospace Engr & Air Traffic Control Gra...
4.6 4.6 (13 lesson ratings) (13)
Given that an isosceles triangle is a triangle with two equal sides; The angles opposite the equal sides are also equal.
So if given one angle is greater then 100 and the other is x
The sum total of angles of any triangle is 180 so we'd have
180 = 100 + x + x
180 = 100 +2x
180 - 100 = 2x
80 = 2x
dividing both sides by 2
80 / 2 = 2x / 2
40 = x
therefore x = 40
Now haven stated that the value for x can't exceed 40 if the other angles is precisely 100. That would mean since the angle give already exceeded 100, the value for x would be less than 40.
Thus x < 40 (d)
Hope this helps
Murtaza N. | Math, Physics, Computer Programming, & Test Prep!Math, Physics, Computer Programming, & T...
First off, you should know that for any triangle, the 3 angles add up to 180:  a + b + c = 180.
Also, if a triangle is isosceles, that means 2 of the 3 angles (as well as 2 of the 3 sides) are the same.
If one of the angles is greater than 100 degrees, neither of the other two can also be greater than 100 (because then just those two angles would add up to more than 200, way more than 180).   The other two angles (x) are equal to each other and are way smaller than 100.
If the angles add up to 180 and one of them is more than 100, the other two must be less than 80 total (again, because they all add to 180).  Since the twin angles are the same and add to less than 80, each must be less than 40.
Which means it's d).  Hope this helps!