Question

The measures of the angles of a triangle are given.
* The measure of angle A is (x + 4) degrees
*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?
A. 32
B. 41
C. 86
D. 68

Answer 1

To solve for \( x \) given the measures of the angles of the triangle, we need to set up the expressions based on the information provided:

1. The measure of angle A is \( A = x + 4 \) degrees.
2. The measure of angle B is twice the measure of angle A, so \( B = 2A = 2(x + 4) = 2x + 8 \) degrees.
3. The measure of angle C is equal to the measure of angle B, so \( C = B = 2x + 8 \) degrees.

According to the triangle angle sum theorem, the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:

\[
A + B + C = 180
\]

Substituting the expressions for angles A, B, and C into the equation:

\[
(x + 4) + (2x + 8) + (2x + 8) = 180
\]

Now, combine the terms:

\[
x + 4 + 2x + 8 + 2x + 8 = 180
\]

This simplifies to:

\[
5x + 20 = 180
\]

Next, isolate \( x \) by subtracting 20 from both sides:

\[
5x = 160
\]

Now, divide by 5:

\[
x = 32
\]

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