2006-10-19 06:59:55 · 10 answers · asked by Lydia 1 in Science & Mathematics ➔ Mathematics
What we really need is a diagram. Are these two angles equal or supplementary? We can tell they are adjacent, and you did mention an isosceles trapezoid, so I'll assume that they are equal angles, but without a diagram it is very possible that you've given us one angle from the top and one from the bottom, in which case they would be supplementary (add to 180°).
If they have equivalent measures, then just equate them:
3x + 10 = 4x - 5
Put the letters on one side, numbers on the other (by adding or subtracting):
10 + 5 = 4x - 3x
15 = x
So x = 15
(And when you plug this back into your equations, you'll see that the angles are both 55°. This means the other two angles (BCD and ADC) are both 125°.)
And if they are supplementary, you would add them and equate them to 180
3x + 10 + 4x - 5 = 180
7x + 5 = 180
7x = 175
x = 25
In this case, the angles would be 85° and 95°.
So compare it to your diagram and take the correct answer.
2006-10-19 07:04:41 · answer #1 · answered by Puzzling 7 · 1⤊ 0⤋
In an isosceles trapezoid, the interior angles are also equal. That is, the two top angles are equal and the two bottom angles are equal. In addition, the two angles connected to one of the equal sides will measure 180 degrees. So, without a picture, your answer will be derived one of two ways.
Method 1:
Assuming that we're talking about the two top angles,
3x+10=4x-5. Adding 5 to both sides and subtracting 3x yields the answer that 15=x.
Method 2:
Assuming the angles are connected to the same isosceles side, then
3x+10 + 4x-5 = 180. Combining like terms on the left gives us
7x+5=180 or 7x=175 or x=25.
You'll have to look at your picture to see which solution is accurate.
2006-10-19 07:12:29 · answer #2 · answered by iuneedscoachknight 4 · 1⤊ 1⤋
An isosceles trapezoid has two equal pairs of congruent angles. The top two would be congruent to one another, and the same for the bottom two angles.
∴ Angle a+ b+c+d = 360°
but any 2 angle are of same measure.
∴ 2(3x+10)+ 2(4x-5) = 360
= 6x+20+8x-10 = 360
= 14x+10 = 360
= 14x = 350
∴ x = 350/14
=25
x= 25
& the angles are 85,85,95,95
2006-10-19 07:30:30 · answer #3 · answered by Venkatesh V S 5 · 0⤊ 0⤋
Since the trapezoid is isosceles, the base angles are equal.
Therefore we have 3x + 10 = 4x - 5. Solving gives x = 15.
2006-10-19 07:04:59 · answer #4 · answered by ironduke8159 7 · 2⤊ 1⤋
15
2016-03-28 01:40:10 · answer #5 · answered by Anonymous · 0⤊ 0⤋
These are one of two solutions here depending on the picture. If the angles are both base angles then they are equal.
So 3x + 10 = 4x - 5
If both angles are on the left or right side they will be supplementary.
so 3x + 10 + 4x - 5 = 180.
It all depends on where the angles lie on the trapezoid.
Hope this helps. :)
2006-10-19 07:21:52 · answer #6 · answered by SmileyGirl 4 · 0⤊ 0⤋
3x + 10 = 4x - 5
3x + 10 - 3x = 4x - 5 - 3x
10 = x - 5
10 + 5 = x - 5 + 5
15 = x
Insert the x value into the equation
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Check
3x + 10 = 4x - 5
3(15) + 10 = 4(15) - 5
45 + 10 = 60 - 5
55 = 55
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2006-10-19 07:12:40 · answer #7 · answered by SAMUEL D 7 · 1⤊ 1⤋
with isosceles always remember two things:
1. equal sides
2. equal base angles
2006-10-19 07:15:01 · answer #8 · answered by csulbalgebra 2 · 0⤊ 0⤋
Everyone's right! You need more info!
2006-10-19 07:16:23 · answer #9 · answered by Anonymous · 0⤊ 0⤋
Picture would help. Thanks.
2006-10-19 07:07:05 · answer #10 · answered by Grover 3 · 2⤊ 1⤋