Questions: Find m angle I in parallelogram GHIJ, m angle I=

Solution Steps

The given figure is a parallelogram $GHIJ$. In a parallelogram, any two consecutive angles are supplementary, which means their sum is 180 degrees. Therefore, $m\angle I + m\angle H = 180^\circ$.

We are given that $m\angle I = 7u - 52^\circ$ and $m\angle H = 2u + 25^\circ$. Substituting these values into the equation from Step 1, we have $7u - 52 + 2u + 25 = 180$

Combining like terms, we have $9u - 27 = 180$ $9u = 180 + 27$ $9u = 207$ $u = \frac{207}{9}$ $u = 23$

Substitute the value of $u$ back into the expression for $m\angle I$: $m\angle I = 7u - 52 = 7(23) - 52 = 161 - 52 = 109^\circ$.

Final Answer