The exterior angle of a triangle is 140°. One of the non-adjacent interior angles is 65°. What is the other non-adjacent interior angle?
A65°
B40°
C75°
D115°
Explanation
📌 Step 1: Recall the Exterior Angle Theorem The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
📌 Step 2: Set up the equation exterior angle = angle A + angle C 140° = 65° + angle C
📌 Step 3: Solve angle C = 140° − 65° = 75°
💡 Tip: The Exterior Angle Theorem is a shortcut! You don't need to find the interior angle at B first. The exterior angle always equals the sum of the two "remote" interior angles.
Question 2 of 10
Florida standards 11A-11DMedium Calc Word Diagram
Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14)
A1695.6 cm³
B565.2 cm³
C339.1 cm³
D452.2 cm³
Explanation
📌 Step 1: Recall the cone volume formula V = (1/3)πr²h
📌 Step 2: Plug in values r = 6 cm, h = 15 cm V = (1/3)(3.14)(36)(15)
💡 Common mistake: Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.
Question 3 of 10
Florida standards 1A-1GHard Calc Word
A flagpole casts a shadow 15 feet long. At the same time, a 6-foot person standing nearby casts a shadow 4 feet long. How tall is the flagpole?
A22.5 feet
B20.0 feet
C24.0 feet
D18.0 feet
Explanation
📌 Step 1: Recognize similar triangles The sun creates the same angle for both the flagpole and the person, making two similar triangles.
📌 Step 2: Set up the proportion flagpole height / flagpole shadow = person height / person shadow h / 15 = 6 / 4
📌 Step 3: Cross-multiply and solve h × 4 = 15 × 6 4h = 90 h = 22.5 feet
💡 Tip: Shadow problems always use similar triangles because the sun's rays are parallel.
Question 4 of 10
Florida standards 1A-1GMedium Calc Word Diagram
A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819)
A141 feet
B164 feet
C115 feet
D186 feet
Explanation
📌 Step 1: Identify the trig ratio We know the hypotenuse (200 ft) and want the opposite side (height). Use sine: sin = opposite / hypotenuse
📌 Step 2: Set up and solve sin(55°) = h / 200 0.819 = h / 200 h = 200 × 0.819 = 163.8
📌 Answer: ≈ 164 feet
💡 Tip: Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.
Question 5 of 10
Florida standards 6A-6EEasy Calc Word Diagram
In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C?
A50°
B60°
C75°
D70°
Explanation
📌 Step 1: Recall the Triangle Angle Sum Theorem All angles in a triangle add up to 180°.
📌 Step 2: Set up the equation ∠A + ∠B + ∠C = 180° 55° + 65° + ∠C = 180°
📌 Step 3: Solve ∠C = 180° − 55° − 65° = 60°
💡 Quick check: 55 + 65 + 60 = 180° ✓
Question 6 of 10
Florida standards 4A-4DEasy Calc Word Diagram
Jake claims: "If a quadrilateral has four right angles, then it must be a square." Which figure below is a counterexample?
ARhombus
BRectangle
CTrapezoid
DSquare
Explanation
A rectangle has four right angles but is NOT necessarily a square (it can have unequal side lengths). The rectangle with sides 90×60 is a counterexample to Jake's claim.
Question 7 of 10
Florida standards 1A-1GEasy Calc Word
A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?
A448 in³
B196 in³
C280 in³
D392 in³
Explanation
📌 Step 1: Identify the shape A pizza box is a rectangular prism (cuboid).
📌 Step 2: Apply the volume formula V = length × width × height V = 14 × 14 × 2
📌 Step 3: Calculate = 392 in³
💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!
Question 8 of 10
Florida standards 7A-7BMedium Calc Word Diagram
In the figure below, DE ∥ BC. If AD = 4, DB = 6, and AE = 5, find EC.
A10.0
B6.0
C8.0
D7.5
Explanation
📌 Step 1: Apply the Triangle Proportionality Theorem Since DE ∥ BC: AD/DB = AE/EC
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD?
ARectangle
BParallelogram
CTrapezoid
DRhombus
Explanation
A quadrilateral with exactly one pair of parallel sides is a trapezoid. AB ∥ DC but AB ≠ DC (16 ≠ 22), confirming it is a trapezoid, not a parallelogram.
Question 10 of 10
Florida standards 9A-9BMedium Calc Word Diagram
From the top of a lighthouse 90 feet tall, the angle of depression to a boat is 28°. How far is the boat from the base of the lighthouse? (tan 28° ≈ 0.532)
A169.2 feet
B203.4 feet
C101.8 feet
D47.9 feet
Explanation
The angle of depression equals the angle of elevation from the boat. tan(28°) = opposite/adjacent = 90/d d = 90/tan(28°) = 90/0.532 ≈ 169.2 feet.