Question

The measures of the angles of a triangle are given.
The measure of angle A is (x + 4).
The measure of angle B is twice the measure of angle A.
/The measure of angle C is equal to the measure of angle B.
What is the value of x? 32, 41, 86, 68?

Answer 1

In a triangle, the sum of the angles is always \(180^\circ\).

Let's denote the angles as follows:
- Measure of angle A: \(A = x + 4\)
- Measure of angle B: \(B = 2A = 2(x + 4) = 2x + 8\)
- Measure of angle C: \(C = B = 2x + 8\)

Now we can set up the equation for the sum of the angles:
\[
A + B + C = 180^\circ
\]
Substituting the expressions for the angles gives us:
\[
(x + 4) + (2x + 8) + (2x + 8) = 180
\]
Simplifying the left side:
\[
x + 4 + 2x + 8 + 2x + 8 = 180
\]
Combine like terms:
\[
(1x + 2x + 2x) + (4 + 8 + 8) = 180
\]
\[
5x + 20 = 180
\]
Now, solve for \(x\):
\[
5x = 180 - 20
\]
\[
5x = 160
\]
\[
x = \frac{160}{5} = 32
\]

So the value of \(x\) is \( \boxed{32} \).