Let's go through the answer choices
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Choice A
Angle R = Angle D ... true; shown by the double tick marks on the angle marker
Angle Q = Angle E ... false; angle Q has a right angle marker while E has a single tick mark on the curved angle marker. The two angles are different
So we can rule out choice A
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Move onto check choice B
Angle R = Angle D ... true; shown by the double tick marks on the angle marker
Angle S = Angle B ... false; similar reasons as above with angle Q and angle E
We can rule out choice B
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Now onto choice C
Angle S = Angle D ... false; the angle D has double tickmarks while angle S has a single tickmark. This indicates they are different in measure. If they were the same, they'd both have single tickmarks together or have double tickmarks together
We can rule out choice C
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Naturally as the only thing left is choice D, it has to be the answer. Let's see if that's the case.
Angle R = Angle D ... true; shown by the double tick marks on the angle marker
Angle S = Angle E ... true; similar as with R and D, but they both have single tickmarks
Angle T = Angle B ... true; both have right angle markers
Angle Q = Angle C ... true; both have right angle markers
So everything matches up properly as expected. Notice how in the sequence TQRS and in BCDE the letters match up in terms of the order they happen in.
T happens first in TQRS, B happens first in BCDE; angle B and T pair up and are congruent corresponding angles
Q happens second in TQRS, C happens second in BCDE; angle Q and C pair up and are congruent corresponding angles
and so on...
So we wouldn't need an image to be able to use this method of matching up the letters like this. This trick works because the two quadrilaterals are similar quadrilaterals.
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Final Answer: Choice D
