In triangle ABC, AB = BC. If angle B contains x degrees, find the number of degrees in angle A
I see that a lot of you don't understand oobleck's response, so I'll elaborate on theirs. Since A = C, that means that you can substitute C in for A, and x for B. So:
A + B + C = 180
A + (x) + (A) = 180
2A + x = 180
2A = 180 - x
A = 180/2 - x/2
A = 90 - x/2
Well, in any triangle, the sum of all three angles is always 180 degrees. Since AB = BC, the angle at B is the same as the angle at C. Let's call the measure of angle B x degrees. That means the measure of angle C is also x degrees.
Now we can find the measure of angle A. Since the three angles in a triangle add up to 180 degrees, we can set up an equation:
x + x + A = 180
Simplifying it, we get:
2x + A = 180
Now, let's solve for A:
A = 180 - 2x
So, the number of degrees in angle A is 180 minus twice the measure of angle B. Now, isn't that angle-tastic?
Since AB = BC, we have an isosceles triangle. In an isosceles triangle, the base angles are equal. Therefore, angle A is also equal to x degrees.
To find the number of degrees in angle A, we first need to understand the properties of the triangle ABC. Since AB is equal to BC, we can say that triangle ABC is an isosceles triangle.
In an isosceles triangle, the two base angles (the angles opposite the equal sides) are congruent. Therefore, angle A is also equal to angle C.
We are given that angle B contains x degrees. Since all three angles in a triangle sum up to 180 degrees, we can set up an equation:
x + A + C = 180 degrees
Since angle A is equal to angle C, we can substitute A for C:
x + A + A = 180 degrees
Combining like terms:
2A + x = 180 degrees
Finally, isolate A by subtracting x from both sides:
2A = 180 degrees - x
Divide both sides by 2 to solve for A:
A = (180 degrees - x) / 2
Therefore, the number of degrees in angle A is (180 degrees - x) divided by 2.
the three angles add up to 180°, so
B+A+C = 180
Now, AB=BC, so C = A.
Now just solve for A.