Question

solve for b.

(b = ?^{\circ})

Explanation:

Identify parallel lines and transversal

The arrows on the two vertical-ish lines indicate that they are parallel. The line segment forming the bottom of the triangle acts as a transversal intersecting these two parallel lines.

Find the alternate interior angle

The angle labeled \(65.5^\circ\) is formed by the transversal and the right-hand parallel line. By the alternate interior angles theorem, the alternate interior angle inside the triangle at the bottom-left vertex is also \(65.5^\circ\).

Apply the triangle angle sum theorem

The interior angles of a triangle always add up to \(180^\circ\). The three interior angles of this triangle are \(b\), \(21.5^\circ\), and \(65.5^\circ\).

Solve for b

We set up the equation:

$$ b + 21.5^\circ + 65.5^\circ = 180^\circ $$

Combine the known angles:

$$ 21.5^\circ + 65.5^\circ = 87^\circ $$

Subtract from \(180^\circ\):

$$ b = 180^\circ - 87^\circ = 93^\circ $$

Answer:

Solve for b.
\(b =\) <blank>93</blank>\(^\circ\)