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
tino4ka555 [31]
3 years ago
14

In the figure above, PQRS is a circle. If PQT and SRTare straight lines, find the value of x.

Mathematics
1 answer:
Elena L [17]3 years ago
4 0

Given:

PQRS is a circle, PQT and SRT  are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

m\angle SPQ+m\angle QRS=180^\circ

81^\circ+m\angle QRS=180^\circ

m\angle QRS=180^\circ-81^\circ

m\angle QRS=99^\circ

Now, SRT  is a straight line.

m\angle QRT+m\angle QRS=180^\circ             (Linear pair)

m\angle QRT+99^\circ=180^\circ

m\angle QRT=180^\circ-99^\circ

m\angle QRT=81^\circ               ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

m\angle PQR=m\angle QRT+m\angle QTR

x=81^\circ+22^\circ

x=103^\circ

Therefore, the value of x is 103 degrees.

You might be interested in
The baseball stadium holds 23,564 people. 3/4 of the seats were sold. How many people were in the stadium
Dennis_Churaev [7]

capacity of the stadium=23564

no.of seats occupied=3/4 of 23564

no.of people in the stadium=23564*3/4

=17673


3 0
3 years ago
Read 2 more answers
Solve the equation for x. x-3/4=12
joja [24]

Answer:

12¾

Step-by-step explanation:

x - ¾ = 12

x = 12 + ¾

c = 12¾ or 12.75

5 0
3 years ago
Read 2 more answers
Please help. with question number 16 ​
ddd [48]

Answer:

12/5

Step-by-step explanation:

All you do is multiply

8 0
3 years ago
Help pls! what is the value of x?
just olya [345]
The X is equal to 3
6 0
3 years ago
Read 2 more answers
What is the value of 5h(-2)+3g(0)?
Ne4ueva [31]
Answer: -10h

I just put it into the calculator
7 0
3 years ago
Read 2 more answers
Other questions:
  • Predict the number of roses in a garden with 16 sunflowers if there are 3 sunflowers in a garden with 81 roses.
    15·2 answers
  • Pls help :> i will give 40 points
    7·2 answers
  • Bob gets 3n+2=20 as the final row of his magic number puzzle table. what was his starting number?
    14·1 answer
  • There are 18 muffins on a plate. If they are split equally among 9 people, how many muffins will each person get?
    14·2 answers
  • If you shift the absolute value parent function, F(x) = |x|, right 9 units, what is the equation of the new function
    12·1 answer
  • Convert radian measurement of 3pi/7 into degrees
    12·1 answer
  • Given: log2 = a, log7 = b. <br> Find: log56
    5·1 answer
  • Find the x- and y-intercepts of<br> 5x - 3y = 12<br> .
    9·1 answer
  • Help please!!!!!!!!!!!!
    8·1 answer
  • Solve the system of equations below
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!