Question

Find measure angle B ( m∠B )

Answer 1

m∠B = 79°

Explanation:

For A given Figure

m∠A = 14x - 11°

m∠B = 8x + 7°

m∠C = 5x + 18°

m∠D = 10x + 13°

Now, For Quadrilateral we know that the sum of all angle in Quadrilateral is 360°

So,

(14x - 11°) + (8x + 7°) + (5x + 18°) + (10x + 13°) = 360°

14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°

Now, Combine Like Terms

i.e.,

14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°

14x + 8x + 5x + 10x - 11° + 7° + 18° + 13° = 360°

37x + 27° = 360°

Now, Subtract 27 from both side

37x + 27° - 27° = 360° - 27°

37x = 333°

Now, Divide 37 from both side

37x/37° = 333°/37°

x = 9°

Here, put the value of x in m∠B

m∠B = 8x + 7° = 8(9) + 7° = 72° + 7° = 79°

Thus, m∠B = 79°

FOR VERIFICATION ONLY:

(14x - 11°) + (8x + 7°) + (5x + 18°) + (10x + 13°) = 360°

37x + 27° = 360°

37(9) + 27° = 360°

333° + 27° = 360°

360° = 360°

Hence, L.H.S = R.H.S

-TheUnknownScientist

Answer 2

Hi there!

m∠B = 79°

The interior angles of a trapezoid always sum up to 360° because a trapezoid is a quadrilateral, so:

360° = (8x + 7)° + (5x + 18)° + (14x - 11)° + (10x + 13)°

Combine like terms:

360° = 37x + 27

Subtract both sides by 27:

333° = 37x

Divide both sides by 37:

x = 9°

Plug in this value of x into the expression for ∠B:

8(9) + 7 = 72 + 7 = 79°