Question

In the figure shown, determine the measures of the marked angles.

​

​

Marked Angle Measure (in degrees) ​
​2x ​
​9x + 4

Answer 1

To find the measures of the marked angles \(2x\) and \(9x + 4\), you will generally need to analyze the geometric configuration given in the figure. Since no figure is provided, I can guide you through a common approach based on typical scenarios in angle measures such as vertical angles, adjacent angles, or angles that add up to a straight line or a circle.

### Step 1: Identify Relationships Between Angles

1. **Adjacent Angles**: If the angles \(2x\) and \(9x + 4\) are adjacent and form a linear pair, then they sum to \(180^\circ\).

\[
2x + (9x + 4) = 180
\]

Simplifying this gives:

\[
2x + 9x + 4 = 180
\]
\[
11x + 4 = 180
\]
\[
11x = 176
\]
\[
x = \frac{176}{11} = 16
\]

Now substituting \(x\) back into the expressions for the angles:

\[
2x = 2(16) = 32^\circ
\]
\[
9x + 4 = 9(16) + 4 = 144 + 4 = 148^\circ
\]

### Step 2: Verify Angle Measures

If these angles were adjacent and form a straight line, they should satisfy:

\[
32 + 148 = 180
\]

So, the measures of the marked angles, if they form a linear pair, are:

- **Marked Angle \(2x\)**: \( 32^\circ \)
- **Marked Angle \(9x + 4\)**: \( 148^\circ \)

### Conclusion

If the angles relate differently (e.g., as vertical angles, or within different relationships), please provide more context or diagrams that clarify how these angles interact, and I can help reevaluate accordingly! For the example posed, under the assumption of a linear relationship, we find:
- **Measure of \(2x\)**: \(32^\circ\)
- **Measure of \(9x + 4\)**: \(148^\circ\)