https://r2.erweima.ai/mathbot/image/1720056602675q8g9jadc.png

The given image provides a parallelogram \( RSTU \) with angles labeled as follows:

- \( \angle R = (6x - 4)^\circ \)
- \( \angle S = (2x + 8)^\circ \)
- \( \angle T = (6x - 4)^\circ \)
- \( \angle U = (2x + 8)^\circ \)

Since \( RSTU \) is a parallelogram, opposite angles are equal, and consecutive angles are supplementary (i.e., they add up to \( 180^\circ \)).

First, we set up the equations using the property that consecutive angles are supplementary:
\[ (6x - 4)^\circ + (2x + 8)^\circ = 180^\circ \]

Simplifying this equation:
\[ 6x - 4 + 2x + 8 = 180 \]
\[ 8x + 4 = 180 \]
\[ 8x = 176 \]
\[ x = 22 \]

Now, we can find each angle:
\[ \angle R = 6x - 4 = 6(22) - 4 = 132 - 4 = 128^\circ \]
\[ \angle S = 2x + 8 = 2(22) + 8 = 44 + 8 = 52^\circ \]
\[ \angle T = 6x - 4 = 128^\circ \] (same as \( \angle R \))
\[ \angle U = 2x + 8 = 52^\circ \] (same as \( \angle S \))

Thus, the measures of each interior angle are:
- \( \angle R = 128^\circ \)
- \( \angle S = 52^\circ \)
- \( \angle T = 128^\circ \)
- \( \angle U = 52^\circ \)

Would you like any further details or have any questions?

Here are five questions you might ask:
1. How do you know that the angles in a parallelogram are supplementary?
2. Can you explain why opposite angles in a parallelogram are equal?
3. How would the approach change if this was a different quadrilateral?
4. Can you solve for the angles if one angle's expression is different?
5. How can this method be applied to solve for unknown angles in other geometric shapes?

**Tip:** Always verify your final answers by checking if they satisfy all given conditions and properties of the geometric figure.

Explore how to find and solve angles in parallelogram RSTU with a step-by-step solution. This problem involves using properties of parallelograms, where opposite angles are equal and consecutive angles are supplementary. Suitable for Grades 9-12 students studying geometry.

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