1. Name the parallelogram: __ 2. If AD=10 , then BC = BC=underline ( ) 3.If AC=15 , then AX= __ 4. If mangle CDA=111^circ then mangle ABC=underline ( ) 5. If mangle DAB=78^circ then mangle ABC= __

## Step 1: Naming the Parallelogram<br />### The parallelogram is named ABCD, where A, B, C, and D are the vertices in order.<br />## Step 2: Finding BC<br />### Given AD = 10, and since opposite sides of a parallelogram are equal, BC = AD. Therefore, BC = 10.<br />## Step 3: Finding AX<br />### AC is a diagonal, and X is the intersection point of the diagonals. Diagonals of a parallelogram bisect each other. Therefore, AX = $\frac{1}{2}$AC. Given AC = 15, AX = $\frac{1}{2}$ * 15 = 7.5.<br />## Step 4: Finding m∠ABC<br />### Given m∠CDA = 111°, and since opposite angles of a parallelogram are equal, m∠ABC = m∠CDA. Therefore, m∠ABC = 111°.<br />## Step 5: Finding m∠ABC (alternate method)<br />### Given m∠DAB = 78°, and since adjacent angles of a parallelogram are supplementary, m∠ABC + m∠DAB = 180°. Therefore, m∠ABC = 180° - 78° = 102°.