# Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

Minor point: the quadrilateral is STWR, not STRW. Vertices are named in order.

The measure of angle T is half the measure of arc WRS. The measure of angle R is half the measure of arc STW. The sum of the measures of the two arcs is the measure of a circle, 360°, so you have

... T + R = (WRS)/2 + (STW)/2

... ... = (WRS + STW)/2

... ... = 360°/2 = 180°

Since the sum of T and R is 180°, they are supplementary.

## Related Questions

Find the measurement of the numbered angles

m<1 = 60

m<2 = 30

m<3 = 80

Step-by-step explanation:

1. Solve for angle (1)

The sum of angles in any triangle is (180) degrees. As one can see, there is a (30) degree angle in this triangle, and a (90) degree angle. Bear in mind that the box around an angle indicates that it is a (90) degree angle. One can form an equation and solve for the unknown angle using this given information;

(30) + (m<1) + (90) = 180

Simplify,

120 + m<1 = 180

Inverse operations,

m<1 = 60

2. Solve for angle (2)

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this theorem here by stating the following,

m<2 = 30

Thus one gets their answer, the measure of angle (2) must be (30) degrees by the vertical angles theorem.

3. Solve for angle (3)

As states above, the sum of angles in a triangle is (180) degrees. Since one has found the measure of angle (2), one can form an equation and solve for the measure of angle (3) using the given information, combined with the information found.

(m<2) + (70) + (m<3) = 180

Susbtitute,

30 + 70 + (m<3) = 180

Simplify,

100 + m<3 = 180

Invers eoperations,

m<3 = 80

Suppose you read online that children first count to 10 successfully when they are 32 months old, on average. You perform a hypothesis test evaluating whether the average age at which gifted children first count to 10 is different than the general average of 32 months. What is the p-value of the hypothesis test? Choose the closest answer.

Step-by-step explanation:

Assuming this info from R

hist(gifted$count) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 21.00 28.00 31.00 30.69 34.25 39.00 ## Sd ## [1] 4.314887 Data given and notation represent the mean represent the sample standard deviation sample size represent the value that we want to test represent the significance level for the hypothesis test. t would represent the statistic (variable of interest) represent the p value for the test (variable of interest) State the null and alternative hypotheses. We need to conduct a hypothesis in order to check if the mean is different than 32, the system of hypothesis would be: Null hypothesis: Alternative hypothesis: If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by: (1) t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value". Calculate the statistic We can replace in formula (1) the info given like this: P-value The first step is calculate the degrees of freedom, on this case: Since is a two sided test the p value would be: You have$1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?$550 in 4%,$450 in 6%
$300 in 4%,$700 in 6%
$700 in 4%,$300 in 6%
$150 in 4%,$850 in 6%

9514 1404 393

$150 in 4%,$850 in 6%

Step-by-step explanation:

The fraction that must earn the highest rate is ...

(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85

That is 0.85 × $1000 =$850 must be invested at 6%. Matches the last choice.

_____

If you let x represent the amount that must earn 6%, then the total interest earned must be ...

x·6% +(1000 -x)·4% = 1000·5.7%

x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000

x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above

Write an equation to solve for x.

x = 50

Step-by-step explanation:

= a straight line is always equal to 180 degrees

= 180 -30 degrees = 150

= 150/3

=50

What is the solution to the equation One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x? x = negative 5 x = negative 4 x = 4 x = 5.

Step-by-step explanation:

The given equation is expressed as

1/4 × x - 1/8 = 7/8 + 1/2 × x

x/4 - 1/8 = 7/8 + x/2

First step is to find the lowest common multiple of the left hand side of the equation and the right hand side of the equation. Then, we would multiply both sides of the equation by the lowest common multiple. The lowest common multiple is 8. Therefore

x/4 × 8 - 1/8 × 8 = 7/8 × 8 + x/2 × 8

2x - 1 = 7 + 4x

7 + 4x = 2x - 1

Subtracting 2x and 7 from the left hand side of the equation and the right hand side of the equation, it becomes

7 - 7 + 4x - 2x = 2x - 2x - 1 - 7

2x = - 8

x = - 8/2 = - 4

Step-by-step explanation:

-4

Circle R has a radius of line segment of QR and QP is a tangent to circle R at point Q.(Picture attached)

(b) What is the value of x? Explain your answer with work.

(c) What is the measure of QRP? Explain your answer with work.

(d) What is the measure of RPQ? Explain your answer with work.

(a) 90°

(b) 8.75

(c) 63.75°

(d) 26.25°

Step-by-step explanation:

(a) A radius to a point of tangency is always perpendicular to the tangent line there. Q is the point of tangency of line PQ, so the segment RQ from the center of the circle, R, to that point makes a 90° angle with PQ. Angle RQP is 90°.

(b) The sum of the acute angles of a right triangle is 90°, so ...

(5x +20)° + (3x)° = 90° . . . . . the sum of the acute angles is 90°

8x + 20 = 90 . . . . . . . . . . . . simplify, divide by °

8x = 70 . . . . . . . . . . . . . . . . . subtract 20

70/8 = x = 8.75 . . . . . . . . . . . divide by the coefficient of x

(c) ∠QRP = (5x+20)° = (5·8.75 +20)° = 63.75° . . . . . use the value of x in the expression for the angle measure

(d) ∠RPQ = (3x)° = (3·8.75)° = 26.25° . . . . . use the value of x in the expression for the angle measure