Write an equation for a in the diagram giving reasons. Solve this equation to find the angles a and B giving reasons.
You know that opposite angles are equal to one another. So the angle of the bottom left-hand corner of the paralleogram is also B. Now, since this B and 3a lie on a line, you know that: $\displaystyle 3a + B = 180$
Also, you know that adjacent angles of a parallelogram are supplementary (they add up to 180). So you have that $\displaystyle a + 82 + B = 180$
Use these equations to solve for a and B.