So let's start with ∡d. Well you know that the two lines with 1 marking on it are parallel so that means 122 = ∡d + 72 because they are alternate interior angles. Hence, ∡d = 50°. Now, let's solve for angle e by the same logic. The two lines with 2 markings on them are both parallel so this means that m∡d = m∡e because they are also alternate interior angles. Hence, m∡e = 50°.
So now, let's take a look at ∡f. You know that the figure there is a parallelogram. Hence, opposite angles are equal. So, m∡f = 3x + 7. You also know that 3x+7 and 4x-2 are same side interior angles meaning that they add to 180. Hence, (3x+7) + (4x-2) = 180; 7x+5 = 180; 7x = 175; x =25°. But, we are not finished. m∡f = 3x + 7, so plug into the formula. This gives you 3(25) +7 = 82° = m∡f.
