1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alborosie
2 years ago
12

In circle T, ∠PTQ ≅ ∠RTS. Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn from point P to poi

nt Q and from point S to point R to form secants P Q and S R. Angles P T Q and S T R are congruent. The measure of arc S R is 66 degrees. The length of T R is 3 and the length of S R is 4. What is the length of PQ? 3 units 4 units 6 units 7 units
Mathematics
1 answer:
Dmitrij [34]2 years ago
7 0

Answer:

The length of PQ is 4 units ⇒ 2nd answer

Step-by-step explanation:

In circle T:

  • TP , TQ , TR , TS are radii
  • PQ and SR are secants
  • The measure of arc SR is 66°
  • ∠PTQ ≅ ∠RTS
  • The length of TR is 3 units
  • The length of SR is 4 units

∵ TP , TQ , TR , TS are radii

- The radii of a circle are equal in length

∴ TP = TQ = TR = TS

∵ TR = 3 units

∴ TQ = 3 units

∴ TP = 3 units

∴ TS = 3 units

∵ ∠RTS is a central angle ⇒ its vertex is the center of the circle

∵ ∠RTS is subtended by arc SR

- The measure of the central angle is equal the measure of

   its subtended arc

∵ The measure of arc SR = 66°

∴ m∠RTS = 66°

∵ ∠PTQ ≅ ∠RTS

∴ m∠PTQ = 66°

In Δs STR and PTQ

∵ ST = PT ⇒ proved

∵ TR = TQ ⇒ proved

∵ m∠PTQ = m∠RTS

- By using SAS case of congruence theorem

∴ Δ STR ≅ Δ PTQ ⇒ SAS congruence theorem

- As a result of congruence

∴ SR ≅ PQ

∵ SR = 4 units

∴ PQ = 4 units

The length of PQ is 4 units

You might be interested in
PLEASE ANSWER ALL QUESTIONS 50 POINTS BRAINLIEST IT'S EASY
Mnenie [13.5K]

Answer:

Here they are Hope this helps :3

Step-by-step explanation:

1. 52

2. 4

7. (im not sure i think its H or A)

7.(not sure think its F)

8.x=6

6 0
2 years ago
If DF+FE=DE, then point F is_________
Dima020 [189]
I believe the correct answer from the choices listed above is option A. If DF+FE=DE, then point F is <span>A. a midpoint of DE (with line over). F is the endpoint of line segment DF and is the starting point of line DE thus it is in between line DE. Hope this answers the question.</span>
8 0
3 years ago
Read 2 more answers
In a school of 910 pupils, 3/7 are boys and 2/5 of the boys wear glasses. how many boys wear glasses?
Wittaler [7]

The number of boys wear glasses are 156 boys.

In this question,

Total number of pupils in the school = 910

Ratio of boys = 3/7

Then, number of boys = 910 × 3/7

⇒ 130 × 3

⇒ 390

Ratio of boys wear glasses = 2/5

Then, number of boys wear glasses = 390 × 2/5

⇒ 78 × 2

⇒ 156

Hence we can conclude that the number of boys wear glasses are 156 boys.

Learn more about word problem here

brainly.com/question/20840435

#SPJ4

6 0
1 year ago
Solve this equation and pick the correct answer
masha68 [24]

Answer:

2.  x = -7/2 and x = 1.

Step-by-step explanation:

2x^2 + 5x - 7 = 0

(2x + 7)(x - 1) = 0

x = -7/2, 1.

6 0
2 years ago
Read 2 more answers
Use the expression, y3 + 4z – 16 to answer the question.
svetlana [45]
Y3 = y x 3 = 4 x 3 = 12
4z = 4 x z = 4 x 6 = 24

12 + 24 - 16

Im using PEMDAS I’m not sure if you use another order of operations if you do just do the expression your way

12 + 24 = 36
36 - 16 = 20

A. 20
8 0
3 years ago
Other questions:
  • There is a child that weighs 90 pounds and every time he eats pizza he gains 5 pounds every week if he ate pizza for 3 weeks how
    9·1 answer
  • How many cubes are in rectangular prism
    15·2 answers
  • I will give you branilest!
    12·1 answer
  • Which relation is a function?
    7·2 answers
  • Which of the following equations is true
    12·2 answers
  • Write a function rule for the statement, “The output is 4 less than the input.” Then, complete the table.
    10·2 answers
  • Angelica writes a function f with a domain of all real numbers and a range of {-13}. Which of the following could be the functio
    7·1 answer
  • Juice wrld is not gone he is i miss juice wrld sippn juice in a better wrld​
    9·2 answers
  • Factor completely 625x8 − 1. (25x4 − 1)(25x4 1) (5x2 − 1)(5x2 1)(25x4 − 1) (5x2 − 1)(5x2 1)(5x2 1)(5x2 1) (5x2 − 1)(5x2 1)(25x4
    14·1 answer
  • Which shape will result from taking a cross section of the tetrahedron through the points shown?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!