Look at the figure, O PORS. Find the mZP,

12
36°
140"
144"

m∠P = 144°

Solution:

PQRS is a parallelogram.

m∠P = 12a°, m∠Q = (4a - 12)° and m∠S = 3a°

In parallelogram, opposite angles are congruent.

m∠Q = m∠S

4a° - 12° = 3a°

Add 12° on both sides.

4a° - 12° + 12° = 3a° + 12°

4a° = 3a° + 12°

Subtract 3a° on both sides.

4a° - 3a° = 3a° + 12° - 3a°

a° = 12°

To find the measure of angle P:

m∠P = 12a°

        = 12(12°)

m∠P = 144°

where are the choices?

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180