Question

1. 12) 14)

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is 180°.

Step2: Solve for question 10

First, find the third - angle of the left - hand triangle: $180-(65 + 60)=55^{\circ}$. Then, consider the right - hand triangle. Let the unknown angle be $x$. We know that $x+35+(50 + 55)=180$. So $x=180-(35 + 105)=40^{\circ}$.

Step3: Solve for question 12

The two triangles are vertical - angle related. The vertical angles are equal. In the lower triangle, the third angle is $180-(35 + 23)=122^{\circ}$. The unknown angle in the upper triangle is equal to the third angle of the lower triangle due to vertical angles. So the unknown angle is $122^{\circ}$.

Step4: Solve for question 14

First, find the adjacent angle to 156° which is $180 - 156=24^{\circ}$. Then, in the triangle with the unknown angle, let the unknown angle be $y$. Using the angle - sum property of a triangle, $y=180-(20 + 35+24)=101^{\circ}$.

Answer:

1. $40^{\circ}$
2. $122^{\circ}$
3. $101^{\circ}$