Question

If ABCD is a parallelogram determine the measure of angle B.
A = (3x), B = (5y - 4)ºC = (9x + 12)​

Answer 1

Respuesta:

The measure of angle B is:

132°

Explicación paso a paso:

On this parallelogram:

A = C

B = D

then:

3x² = 9x+12

3x² - 9x - 12 = 0

x = {-(-9)±√((-9²)-(4*3*-12))} / (2*3)

x = {9±√(81+144)} / 6

x = {9±√225} / 6

x = {9±15} / 6

This is a geometrical figure then only takes the positive value:

x = {9+15} / 6

x = 24/6

x = 4

then:

A = 3x²

A = 3*4²

A = 3*16

A = 48°

A = B

B = 48°

On a parallelogram the sum of the internal angles results 360°

A + B + C + = 360°

and:

B = D

then:

48 + 48 + B + B = 360

96 + 2B = 360

2B = 360 - 96

2B = 264

B = 264/2

B = 132°