Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to calculate the measure of ∠opq? circle n is shown with a quadrilateral opqr inscribed inside it. angle o is labeled x plus 16. angle p is not labeled. angle q is labeled 6x minus 4. angle r is labeled 2x plus 16.

answer choices
∠opq + (2x + 16)° = 180°
m∠opq = (6x − 4)° + (2x + 16)°
m∠opq + (x + 16)° + (6x − 4)°= 360°
m∠opq = (x + 16)° + (6x − 4)°

first option.

Step-by-step explanation:

By definition, the sum of opposite angles in a quadrilateral inscribed in a circle is 180°.

Observe the figure.

You can notice that the angle   and the angle are opposite, which means that they sum is 180°.

Knowing this, you can write the following equation:

Based on the figure, you know that:

Therefore, substituting this into the equation ,  you get the following equation that can be used to calculate the measure of :

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

nope lol

step-by-step explanation: