Question

1. find the measure of angle b.

10)
11)
12)

Explanation:

Step1: Identify angle - relationships

For question 9:
We know that a straight - line angle is 180°. If we consider the angle adjacent to the 50° angle and angle b, they form a straight - line. So, $b = 180^{\circ}-50^{\circ}$.
For question 10:
Vertical angles are equal. The angle with measure 43° and angle b are vertical angles. So, $b = 43^{\circ}$.
For question 11:
First, note that the non - labeled angle adjacent to 96° and 209° forms a full - circle (360°). Let's find the non - labeled angle. The sum of angles around a point is 360°. Let the non - labeled angle be $x$. Then $x+96^{\circ}+209^{\circ}=360^{\circ}$, so $x = 360^{\circ}-96^{\circ}-209^{\circ}=55^{\circ}$. Angle b and $x$ are vertical angles, so $b = 55^{\circ}$.
For question 12:
If we assume the two angles 63° and b are complementary (since no other information about the overall angle relationship is given and they seem to be part of a right - angle or a 90° situation), then $b=90^{\circ}-63^{\circ}$.

Step2: Calculate angle values

For question 9:
$b = 130^{\circ}$
For question 10:
$b = 43^{\circ}$
For question 11:
$b = 55^{\circ}$
For question 12:
$b = 27^{\circ}$

Answer:

1. $130^{\circ}$
2. $43^{\circ}$
3. $55^{\circ}$
4. $27^{\circ}$