Question

(not just the \?\ angle.)
14)
16)

Explanation:

Step1: Solve for top triangle's missing angle

Sum of angles in triangle is $180^\circ$.
$\text{Missing angle} = 180^\circ - 43^\circ - 84^\circ = 53^\circ$

Step2: Identify vertical angle for lower triangle

Vertical angles are equal, so the corresponding angle in the lower triangle is $53^\circ$.

Step3: Solve for "?" in problem 14

Sum of angles in triangle is $180^\circ$.
$\text{?} = 180^\circ - 97^\circ - 53^\circ = 30^\circ$

Step4: Solve for top triangle's missing angle (16)

Sum of angles in triangle is $180^\circ$.
$\text{Missing angle} = 180^\circ - 35^\circ - 55^\circ = 90^\circ$

Step5: Identify vertical angle for lower triangle (16)

Vertical angles are equal, so the corresponding angle in the lower triangle is $90^\circ$.

Step6: Solve for "?" in problem 16

Sum of angles in triangle is $180^\circ$.
$\text{?} = 180^\circ - 90^\circ - 58^\circ = 32^\circ$

Answer:

Problem 14: $30^\circ$
Problem 16: $32^\circ$