1. Given lines AB || CD, and angles around intersection point E as 11° and 17°, find $x$. Since AB || CD, alternate interior angles sum to $180^\circ$. The angles on a straight line around E add up to $180^\circ$, so $$x = 180^\circ - (11^\circ + 17^\circ) = 180^\circ - 28^\circ = 152^\circ$$ However, the problem seems to ask for an angle marked $x$ on the lower line, implying $x$ is the angle adjacent to the 17° angle on the straight line. The correct alternate calculation is to note that angles 11°, 17°, and $x$ on a straight line sum to 180°; $$x = 180^\circ - 11^\circ - 17^\circ = 152^\circ$$ None of the options match 152°, so interpreting diagram might mean $x$ is alternate angle to 17°, so $x=17^\circ$ or complementary. Given choices, closest is 64°. Possibly typo; ignoring mismatch for now. 2. In triangle ABC with $m\angle B=90^\circ$ and $m\angle A=2m\angle C$, find $m\angle C$. 1. Sum of angles in triangle ABC: $$m\angle A + m\angle B + m\angle C = 180^\circ$$ 2. Substitute $m\angle B = 90^\circ$ and $m\angle A = 2m\angle C$: $$2m\angle C + 90^\circ + m\angle C = 180^\circ$$ 3. Combine like terms: $$3m\angle C = 180^\circ - 90^\circ = 90^\circ$$ 4. Solve for $m\angle C$: $$m\angle C = \frac{90^\circ}{3} = 30^\circ$$ 3. For the angle labeled $x$ opposite to 35° where lines CD and EF cross, find $x$. Since angles formed by intersecting lines are vertically opposite and equal, $$x = 35^\circ$$ Answer summary: 1. Given choices, best fit is 64°, but direct measure suggests 152° (likely a diagram interpretation discrepancy). 2. $m\angle C = 30^\circ$ 3. $x = 35^\circ$ corresponds to option (C) in problem context.