Question

what is ( mangle b )?
options:
a. 51
b. 129
c. 134
d. 141

Explanation:

Step1: Determine the number of sides (n) of the polygon.

The given figure is a heptagon (7 - sided polygon), so \( n = 7 \).

Step2: Calculate the sum of interior angles of a heptagon.

The formula for the sum of interior angles of a polygon is \( (n - 2)\times180^{\circ} \).
Substituting \( n = 7 \), we get \( (7 - 2)\times180^{\circ}=5\times180^{\circ} = 900^{\circ} \).

Step3: Identify the known angles.

The known angles are: \( \angle A = 120^{\circ} \), \( \angle G = 129^{\circ} \), \( \angle F = 130^{\circ} \), \( \angle E = 142^{\circ} \), \( \angle C = 148^{\circ} \), and \( \angle D = 90^{\circ} \) (since it is a right angle).

Step4: Let \( \angle B = x \) and sum all angles to equal \( 900^{\circ} \).

So, \( 120^{\circ}+129^{\circ}+130^{\circ}+142^{\circ}+148^{\circ}+90^{\circ}+x = 900^{\circ} \).

Step5: Calculate the sum of the known angles.

\( 120 + 129 + 130 + 142 + 148 + 90 = 120+129 = 249; 249+130 = 379; 379+142 = 521; 521+148 = 669; 669+90 = 759 \).

Step6: Solve for \( x \).

\( 759 + x = 900 \), so \( x = 900 - 759 = 141^{\circ} \).

Answer:

D. 141