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

Transcript text: Find $m \angle I$ in parallelogram GHIJ, \[ m \angle I= \]

Solution

Solution Steps

Step 1: Consecutive angles of a parallelogram are supplementary.

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

Step 2: Set up the equation.

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 $7u - 52 + 2u + 25 = 180$

Step 3: Solve for u.

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

Step 4: Find the measure of angle I.

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