Question 45 Answer and Explanation _ACT OG5 Form 67A Math Section

Use the following information to answer questions 44-46.

In the figure below, △ACB is a right triangle with legs of length a units and b units, where 0 < a < b, and hypotenuse of length c units. The triangles △YCA, △ZBA, and △XCB are equilateral. The area of an equilateral triangle with sides x units long is $\frac{\sqrt{3}}{4}{x}^{2}$ square units.

45. For all values of a and b such that 0 < a < b, which of the following lists the angles ∠XCY, ∠CAZ, and ∠CBZ in order of their measures from least to greatest?

A. ∠CBZ, ∠XCY, ∠CAZ

B. ∠CBZ, ∠CAZ, ∠XCY

C. ∠XCY, ∠CAZ, ∠CBZ

D. ∠CAZ, ∠CBZ, ∠XCY

E. ∠CAZ, ∠XCY, ∠CBZ

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

Because the three triangles next to the right triangle are equilateral triangles, so ∠XCY=360-60-90-60=150=60+90, ∠CAZ=60+∠CAB, ∠CBZ=60+∠ABC . Because a