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
Allisa [31]
2 years ago
13

Find the measures of each angle in the inscribed quadrilateral.

Mathematics
1 answer:
Marat540 [252]2 years ago
8 0

Answer:

m∠P = 55° , m∠R = 125° , m∠Q = 110° , m∠S = 70°

Step-by-step explanation:

* Lets study the figure

- A circle and inscribed quadrilateral PQRS

- The four vertices of the quadrilateral lie on the circumference

 of the circle

∴ PQRS is a cyclic quadrilateral

* Lets revise the properties of the cyclic quadrilateral

- Each two opposite angles are supplementary, that means

 the sum of each two opposite angles = 180°

- The measure of the exterior angle = the measure of the

  opposite interior angle

* Lets solve the problem

∵ PQRS is a cyclic quadrilateral

∴ m∠P + m∠R = 180° ⇒ opposite angles

∵ m∠P = 5y + 30

∵ m∠R = 15y + 50

∴ 5y + 30 + 15y + 50 = 180 ⇒ add the like terms

∴ 20y + 80 = 180 ⇒ subtract 80 from both sides

∴ 20y = 100 ⇒ divide both sides by 20

∴ y = 5

* Now lets substitute the value of y in each angle to find

 their measures

∵ m∠P = 5y + 30

∴ m∠P = 5(5) + 30 = 25 + 30 = 55°

∵ m∠R = 15y + 50

∴ m∠R = 15(5) + 50 = 75 + 50 = 125°

∵ m∠Q = y² + 85

∴ m∠Q = 5² + 85 = 25 + 85 = 110°

∵ ∠S is opposite to ∠Q

∴ m∠S + m∠Q = 180° ⇒ opposite angles in the cyclic quadrilateral

∴ m∠S + 110 = 180 ⇒ subtract 110 from the both sides

∴ m∠S = 70°

* The measures of the angles are

  m∠P = 55° , m∠R = 125° , m∠Q = 110° , m∠S = 70°

You might be interested in
-7x^3-9x^2+8x this is factoring completely
loris [4]
Answer:
<span> (x + 6) • (x + 5) • (x - 2)

Is this what u were looking for? Sorry if not XDD

</span>
3 0
3 years ago
Read 2 more answers
Bonita said that the product of 5/6 times 1 2/3= 7/3. How can you tell that her answer is wrong?
Masja [62]

Answer:

B. 5/6 of a number cannot be greater than the number.

7/3 = 2 1/3 > 1 2/3

6 0
2 years ago
Which of the following could be the lengths of the sides of a 30°-60°-90° triangle?
Inga [223]
According to Pythagoras theorem

a^2+b^2=c^2

similarly ,

3^2+ 4^2= 5^2

9+16=25
25=25

LHS=RHS
so angle of triangle is 30 , 60 and 90

answer is 3,4,5
7 0
3 years ago
Read 2 more answers
Help please this question is so hard!
Nitella [24]
So to solve this first you need to convert all the answers to decimals.
Site B 17/9 = 1.89 when you round up
Site D 4/3 = .75
Then look at all the numbers least to greatest.
D .75 m C 1.36 m A 1.60 m B 1.89 m
Answer D, C, A, B
6 0
2 years ago
Krishna has $4.90 with a combined 34 nickels and quarters. How many of<br> each coin does she have?
Oksana_A [137]

Answer:

Step-by-step explanation:

-34 nickles is = 1.70

34 quarter is  = 8.50

1.70 plus 8.50 plus 4.90 = 15.1 i think

7 0
3 years ago
Other questions:
  • Math Help
    15·2 answers
  • Laura drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when laura drove
    6·1 answer
  • Please Help! i am on the last stretch for a test, and i seriously need help with this question. i know its lame, but i really am
    6·2 answers
  • Sandy earns $4.35 per hour in base (cash) pay while waiting tables at the MegaBurger Health Food Restaurant. Sandy earns on aver
    10·1 answer
  • A student solved this problem and said the answer was 78.
    15·2 answers
  • SOMEONE PLEASE HELP. !! ASAP!! NO BULL ANSWERS !!<br><br>​
    10·2 answers
  • Find the median and mean of the data set below:<br> 5, 7, 3, 36, 7, 23<br> Ed
    10·2 answers
  • If a rectangle A has sides are three times the length of those rectangle B, how do the areas of the two rectangles compare?
    11·1 answer
  • Rewrite the polynomial in the form ax^2+bx+c and then identify the values of a, b, and c
    13·1 answer
  • Three friends go to a store to rent games and movies. Calvin rents 3 movies and 2 video games and spends a total of $25. Samanth
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!