Question

10)
12)
14)

Explanation:

Step1: Find missing angle in left triangle

The sum of angles in a triangle is $180^\circ$. For the left triangle with angles $60^\circ$, $65^\circ$, and the unknown angle (let's call it $x$):
$x = 180^\circ - 60^\circ - 65^\circ = 55^\circ$

Step2: Find adjacent angle to $x$

$x$ and the adjacent angle (let's call it $y$) form a straight line, so they are supplementary:
$y = 180^\circ - 55^\circ = 125^\circ$

Step3: Find the unknown angle in right triangle

The sum of angles in the right triangle is $180^\circ$. Let the unknown angle be $z$:
$z = 180^\circ - 35^\circ - 125^\circ = 20^\circ$

Step4: Find missing angle in lower triangle

The sum of angles in the lower triangle is $180^\circ$. Let the unknown angle be $w$:
$w = 180^\circ - 35^\circ - 23^\circ = 122^\circ$

Step5: Find vertical angle of $w$

Vertical angles are equal, so the angle opposite $w$ is also $122^\circ$.

Step6: Find the unknown angle in upper triangle

The sum of angles in the upper triangle is $180^\circ$. Let the unknown angle be $v$:
$v = 180^\circ - 27^\circ - 122^\circ = 31^\circ$

Answer:

For question 10: $20^\circ$
For question 12: $31^\circ$