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 vale of X

Answer 1

To solve for \( x \) in the problem provided, we need to set up an equation based on the measures of the angles in a triangle. The sum of the angles in a triangle is always \( 180^\circ \).

Let’s define the angles based on the information given:

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

Now, we can express the sum of the angles:

\[
A + B + C = 180^\circ
\]

Substituting the expressions for \( A \), \( B \), and \( C \):

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

Now, simplify the equation:

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

Combine like terms:

\[
x + 2x + 2x + 4 + 8 + 8 = 180
\]
\[
5x + 20 = 180
\]

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

\[
5x = 160
\]

Now, divide by 5:

\[
x = 32
\]

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