Quant Practice Questions for ACT - 4 | Mathematics for ACT PDF Download

Ans: AC is a diameter and ADC is a semi-circle whose measure is 180°.

Note: Any angle inscribed in a semi-circle is aright angle.

Ans: BC is a diameter (a chord that passes through the center of the circle forming 2 equal arcs of 180 ° each). Angle B is an inscribed angle. The measure of AC is 60° and the measure of BAC is180°. Therefore:

Ans: Find x by using the equation:

x = 70°
Since y is the measure of an inscribed angle, it measures 1/2 (x) = 35°

Ans: A regular hexagon is a polygon whose six sides and six angles are congruent. Its central angle measures 60° (360 ÷ 6 = 60°). Triangle AOB is isosceles and ∠OAB = ∠OBA. A regular hexagon contains 6 equilateral triangles. Thus x = 8. An inscribed angle is an angle whose vertex is on the circle and whose sides are chords of the circle. A chord is a line drawn within a circle touching two points on the circumference of the circle.

Ans: To find x, find the number of degrees in the central ∠AOB. OA and OB are radii in the same circle and are, therefore, equal. The angles opposite these equal sides are equal, so m ∠B = 62°

Since central ∠AOB measures 56°, its intercepted arc measures 56°

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Ans: Since radius = 5, diameter = 10
C = πd
C = (3.14)(10)
C = 31.4”

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Ans: DF is the side opposite the 30° angle, so its measure is one-half the hypotenuse. Since EF = 4, DF = 2. DE is the side opposite the 60° angle, so its measure is one-half the hypotenuse times √3 .