What is the measure of angle B in the triangle?

Angle B measures 70 degrees

Step-by-step explanation: One angle is given as 40 while the other two angles are yet unknown.

Remember that the sum of the interior angles in a triangle equals 180 degrees. In other words

Angle A + Angle B + Angle C = 180

Therefore

40 + (2x - 30) + (x + 20) = 180

40 + 2x - 30 + x + 20 = 180

By collecting like terms we have

40 - 30 + 20 + 2x + x = 180

30 + 3x = 180

Subtract 30 from both sides of the equation

3x = 150

Divide both sides of the equation by 3

x = 50

Having calculated x = 50 we can now compute the value of angle B as follows;

When x = 50,

2x - 30 becomes

2(50) - 30

= 100 - 30

= 70.

Angle B measures 70 degrees

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft