If 1=3 2=3 3=5 4=4 5=4 Then, 6=?

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

Elena L [17]

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.

4 0

3 years ago

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one sam

____ [38]

We can set up 2 equations given the information.
Let the price of advance ticket be represented by A and same day ticket by S

A + S = 50
20A + 40S = 1700

Solve for A in the first equation by subtracting S on both sides.
U will get A = 50 - S

Now substitute 50 - S for A in the second equation.

20 (50 - S) + 40S = 1700
1000 - 20S + 40S = 1700
20S = 700
S = 35

Same day ticket costs $35 and advance ticket costs $15

6 0

3 years ago

One estimate of the population of the world on January 1, 2005, is

inn [45]

Answer:

8,566,379,470 people

Step-by-step explanation:

Let's start simple. In order to find the population increase on January 1, 2006, we need to multiply 6,486,915,022 by 1.4% and add it to 6,486,915,022.