ray EC bisects angle BED, The measure of angle AEB equals 11x minus 12.and The measure of angle CED equals 4x plus 1.. Find measure of angle AEC.
You first have to find x.
To find x, we need to add all the angles together to get 180°.
Since EC bisects BED, we know angle BEC and CED equal the same measure.
AEB + BEC + CED = 180°
(11x - 12) + (4x + 1) + (4x + 1) = 180°
Add like terms and solve
19x - 10 = 180
19x = 190
x = 10
Now, we substitute 'x' in AEB and BEC
AEB = 11x - 12
11 (10) - 12
AEB = 98
BEC = 4x + 1
4 (10) + 1
BEC = 41
98 + 41 = 139
AEC = 139
Hope this helps!
Thanks man
I am pergent and my water just broke my partens do not know
preciate it bob
Well, it seems like we have a bit of a geometry problem here. Let's see if we can put on our clown noses and solve it!
Since ray EC bisects angle BED, angle AEC and angle CED are equal.
So, we can set their measurements equal to each other:
11x - 12 = 4x + 1
Now, let's simplify this equation:
11x - 4x = 1 + 12
7x = 13
x = 13/7
Now that we've found the value of x, we can substitute it back into one of the expressions to find the measure of angle AEC:
Measure of angle AEC = 11(13/7) - 12
But tell you what, I'm feeling extra clowny today! So, I'll just go ahead and crunch the numbers for you:
Measure of angle AEC ≈ 20.9 degrees.
There you have it! The measure of angle AEC is approximately 20.9 degrees.
To find the measure of angle AEC, we need to apply the Angle Bisector Theorem.
The Angle Bisector Theorem states that when a ray divides an angle into two congruent angles, the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the measures of the two smaller angles formed.
In this case, ray EC bisects angle BED, which means that angle AEC and angle CED are congruent.
Therefore, we can set up the following equation to represent the Angle Bisector Theorem:
Measure of angle AEC / Measure of angle CED = Length of segment AE / Length of segment CE
Let's substitute the given measures:
(Measure of angle AEC) / (4x + 1) = Length of segment AE / Length of segment CE
We also know that the sum of the measures of angle AEB and angle CED is equal to the measure of angle BED:
Measure of angle AEB + Measure of angle CED = Measure of angle BED
Substituting the given measures:
(11x - 12) + (4x + 1) = Measure of angle BED
Simplifying the equation:
15x - 11 = Measure of angle BED
Now, since ray EC bisects angle BED, angle AEC is congruent to angle CED, so we can rewrite the equation as follows:
15x - 11 = 2(4x + 1)
Now, solve the equation for x:
15x - 11 = 8x + 2
15x - 8x = 2 + 11
7x = 13
x = 13/7
Now that we have the value of x, we can substitute it back into the equation to find the measure of angle AEC:
Measure of angle AEC = 4x + 1
Measure of angle AEC = 4(13/7) + 1
Measure of angle AEC = (52/7) + 1
Measure of angle AEC = 52/7 + 7/7
Measure of angle AEC = 59/7
Therefore, the measure of angle AEC is 59/7.
Can't tell whether A is in between B and E or not.
But, you know that BEC=BED
That should help you pin down AEC.
If A is between B and C
BEA+AEC=BEC
11x-12 + AEC = 4x+1
AEC = 13-7x
or, if B is between A and C,
AEC-AEB=BEC
AEC-11x+12 = 4x+1
AEC = 15x-13
Of course, A could be a lot of other places, too.