SAT MATH PROBLEMS ON ANGLES

Problem 1 :

In the figure above, what is the value of x?

A)  140

B)  160

C)  190

D)  230

Solution :

Problem 2 :

In the figure above, what is the values of y?

A)  52

B)  60

C)  68

D)  76

Solution :

Problem 3 :

In the figure above, ray OB bisects ∠COA. If m∠DOB = 11x + 6 and m∠COA = 8x - 12, what is the measure of ∠DOC?

A)  92

B)  96

C)  102

D)  108

Solution :

Problem 4 :

In the figure above, m∠ABE = 120° and m∠CBD = 135°. What is the measure of ∠DBE?

A)  63

B)  68

C)  75

D)  79

Solution :

Problem 5 :

In the figure shown above, m∠POQ = 55°.

Find each of the following :

a)  m∠SOT

b)  m∠ROT

c)  m∠POT

d)  m∠POR

Solution :

Problem 6 :

In the figure above (figure given in video), ℓ || m. What is the value of x?

A)  45

B)  50

C)  55

D)  60

Solution :

Problem 7 :

In the figure above (figure given in video), ℓ || m. What is the value of x?

A)  120

B)  125

C)  130

D)  135

Solution :

Problem 8 :

In the figure above, lines ℓ and m are parallel and BD bisects ∠ABC. What is the value of x?

A)  54

B)  60

C)  68

D)  72

Solution :

Problem 9 :

In the figure above, DA || BC and AB bisects ∠DAC. What is the measure of ∠BCA in terms a?

A)  180 - a

B)  2a - 180

C)  180 - 2a

D)  2a - 90

Solution :

Problem 10 :

In the figure above, lines m and n are parallel, Find the value of x.

Solution :

Problem 11 :

In the figure above, r || t. What is the value of x + y?

A)  37

B)  40

C)  43

D)  46

Solution :

Problem 12 :

In the figure above, m || n. If a = 50 and b = 120, what is the value of c?

A)  50

B)  60

C)  70

D)  80

Solution :

Problem 13 :

In the figure above, lines ℓ, m, and n are parallel. What is the value of x + y?

A)  160

B)  200

C)  230

D)  290

Solution :

Problem 14 :

In the figure above, ℓ || m. What is the value of x?

A)  30

B)  35

C)  40

D)  45

Solution :

Problem 15 :

In the figure below, ℓ || m, r ⊥ t and m∠1 = 32. Lines ℓ, r, and t intersect at one point. Find the following angle measures :

(i)  m∠2

(ii)  m∠3

(iii)  m∠4

(iv)  m∠5

Solution :

Problem 16 :

In the figure above, AB || CD and BC || DE. What is the value of x?

A)  47

B)  51

C)  55

D)  57

Solution :

Problem 17 :

In the figure above, r || t. What is the value of a + b?

A)  160

B)  175

C)  185

D)  200

Solution :

Problem 18 :

In the figure above, what is the value of x?

Solution :

Problem 19 :

In the figure above, PQ is parallel to ST. What is the measure of ∠QRS?

Solution :

Problem 20 :

In the figure above, find the value of x.

Solution :

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