10 !

quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle r? you must show all work and calculations to receive credit.

∠ R = 137°.

Step-by-step explanation:

For any four-sided quadrilateral inscribed inside a circle the sum of the opposite angles are always 180°.

Now, see the diagram given with the question.

We have ∠ P + ∠ R = 180°

⇒ (3y + 8) + y = 180

⇒ 4y = 180 - 8

⇒ 4y = 172

⇒ y = 43

Therefore, the value of the angle R is 3y +8 = 3(43) + 8 = 137° (Answer)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.