In a rhombus, opposite angles are equal, and the sum of all interior angles is 360 degrees. Given that two angles measure 104 degrees and the other angle measures 76 degrees, we can find the measure of angle \( x \).
Since the angles in a rhombus are opposite, the angles can be paired as follows:
- One pair: \( 104^\circ \) and \( 104^\circ \)
- Another pair: \( 76^\circ \) and \( x \)
The sum of the angles in a rhombus can be represented as:
\[ 104 + 104 + 76 + x = 360 \]
Calculating the known angles:
\[ 104 + 104 + 76 = 284 \]
Now we can set up the equation:
\[ 284 + x = 360 \]
To isolate \( x \), subtract 284 from both sides:
\[ x = 360 - 284 \]
Calculating:
\[ x = 76 \]
So, the measure of angle \( x \) is:
\[ \boxed{76} \] degrees.
1 answer