Geometry and TrigonometryVery hardAngle in a regular polygon's diagonal
Geometry and Trigonometry practice question
In a regular hexagon ABCDEF, what is the measure of angle ACD, formed by diagonal AC and side CD?
- A. 90°Correct
- B. 60°
- C. 120°
- D. 30°
Answer: A. 90°
Each interior angle of a regular hexagon is 120°. Triangle ABC is isosceles with apex angle 120°, so angle BCA = 30°. Then angle ACD = 120 − 30 = 90°.
Why the other answers are wrong
- B. 60°
- 60° is the exterior angle of the hexagon.
- C. 120°
- 120° is the full interior angle at C, but diagonal AC cuts off 30° of it.
- D. 30°
- 30° is angle BCA, the part cut off, not the remainder.
More Geometry and Trigonometry questions
- Very hard
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is N… - Very hard
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the valu… - Very hard
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Very hard
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Very hard
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this c… - Very hard
What is the perimeter of triangle ABC?
Not affiliated with the College Board. SAT is a trademark of the College Board.