Solving Angles
Find the missing angle: Two lines intersect forming vertical angles; one angle measures 42°. What is the measure of the vertical opposite angle?
42°
Given a circle, an arc measures 60°. What is the measure of the central angle that subtends that arc?
(subtends: the legs of the angle meet at the endpoints of the intercepted arc)
60°
Find the volume of a cube with side length 4 cm.
64 cm3
Find the diagonal of a rectangle with side lengths 3 and 4.
5
Name the four congruency shortcuts for triangles.
SSS, SAS, ASA and SAA
Find the area of a sector with central angle 90° in a circle of radius 6.
9pi
Define "congruent."
"Congruent": identical in shape and size.
On a straight line, angles A and B are adjacent and form a linear pair. If angle A = 3x + 10 and angle B = 2x + 40, find x and angle A.
x = 26o; angle A = 88°
A semicircle has arc measure _____.
180°
Find the surface area of a rectangular prism with dimensions 3 cm by 4 cm by 6 cm.
Surface area = 2(3⋅4+3⋅6+4⋅6)=2(12+18+24)=2(54)=108 cm2
Find the diagonal of a rectangular prism with dimensions 2, 3, and 6.
7
True or False: If triangle BOY is congruent to triangle GRL then segment OY is congruent to segment LG
FALSE!
A sector has area 12π and radius 4. Find the central angle in degrees.
270o
Which point of concurrency is the intersection of perpendicular bisectors?
Perpendicular bisectors intersect at the circumcenter.
Two parallel lines are cut by a transversal. If a corresponding angle is 56°, what is the measure of its alternate interior angle?
56°
True or False: The circumference of a circle is more than three times the length of the diameter.
TRUE!
Find the volume of a regular square pyramid with base side 6 and height 9. (Give exact value.)
Volume = (1/3)⋅62⋅9 = (1/3)⋅36⋅9 = 108
True or False: Cosine is the ratio of opposite over hypotenuse.
FALSE!
Given triangle ABC similar to triangle DEF with ratio of similarity 1/2, if AB = 10, find DE.
DE = 5
Find the area of a regular hexagon with side length 6 and an apothem of
3sqrt(3)
54sqrt3
Define "central angle," "inscribed angle," and give one relationship between them.
central angle: vertex at center
inscribed: vertex on circle
Inscribed angle = half the measure of its intercepted arc/central angle.
In triangle ABC, angle A = 35°, angle B = 65°. Find angle C. Then classify the triangle by angles.
angle C = 80°; acute triangle
A chord subtends a 40° central angle. What is the measure of the intercepted minor arc?
If the circle’s radius is 10, what is the arc length? (Use terms of pi.)
arc = 40°
arc length = 40/360⋅2π(10) = 1/9(2)π(10) = (20/9)π
Compute the volume of a triangular prism with base area 10 and height 8.
80/3 or 26.67
(V = 1/3 B h)
Using SOH CAH TOA: In a right triangle, if opposite = 4 and hypotenuse = 5, what is sin(θ)?
sin(θ)=4/5=0.8
Given triangles with sides 7, 24, 25 and 14, 48, 50, determine if they are similar, congruent, or neither. Explain.
They are similar (each side doubled), not congruent.
Find the area of a trapezoid with bases 8 and 14 and height 5.
55
Where is the orthocenter located in an acute triangle? In an obtuse triangle?
Orthocenter is inside an acute triangle and outside an obtuse triangle.
In quadrilateral WXYZ, angle W = 110°, angle X = 85°, angle Y = 95°. Find angle Z. Is the quadrilateral possibly cyclic (opposite angles supplementary)? Explain.
angle Z = 70°; opposite angles 110° and 70° are not supplementary so not cyclic
An inscribed angle measures 35°. What is the measure of its intercepted arc?
If another inscribed angle intercepts the same arc, what is its measure?
intercepted arc = 70°; other inscribed also 35°
Find the surface area and volume of a cube of side 5. Then explain how changing side length by factor 2 affects volume and surface area.
Cube SA = 6(52)=150; V = 53 = 125
Doubling side -> SA ×4, V ×8.
A ladder leans against a wall making a 65° angle with the ground; ladder length is 20 ft. How high does it reach on the wall?
(Use trig ratio; round to 1 decimal.)
height = 20sin(65∘)≈18.1 ft
If G is the centroid in a triangle, state the ratio of segments along a median from vertex to centroid to midpoint of opposite side.
G is centroid; median divided in 2:1 ratio from vertex to centroid to midpoint.
A polygon has interior angle measure 156° for each vertex and is regular. How many sides does the polygon have?
15
True or False: In a right triangle, the ratio of the length of the side opposite acute angle A to the length of the side adjacent to angle A is called the tangent of angle A.
TRUE!