Let's solve for the missing angles in each of the given figures.

1. Triangle with angles 70° and 50°:

We need to find angle $a$.

In a triangle, the sum of the interior angles is always 180°. $a + 70^\circ + 50^\circ = 180^\circ$ $a = 180^\circ - 70^\circ - 50^\circ$ $a = 60^\circ$ So, angle $A = 60^\circ$.

2. Triangle with angles 34° and 78°:

We need to find angle $Z$.

Again, the sum of the interior angles in a triangle is 180°. $Z + 34^\circ + 78^\circ = 180^\circ$ $Z = 180^\circ - 34^\circ - 78^\circ$ $Z = 68^\circ$ So, angle $Z = 68^\circ$.

3. Circle with central angle and intersecting chords:

Given: $\angle AOD = 33^\circ$ and we need to find $\angle B$.

To solve this problem, we need to understand the properties of angles in a circle.

• The central angle $\angle AOD = 33^\circ$.
• $\angle AOD$ subtends the arc $AD$.
• The angle at the circumference subtended by the same arc ($\angle ABD$) is half of the central angle.

$\angle ABD = \frac{1}{2} \times 33^\circ = 16.5^\circ$

For angle $\angle B$, we use the fact that angles subtended by the same arc are equal.

Since $\angle ABD$ is the angle at the circumference subtended by arc $AD$, and $\angle B$ is the same arc subtended at point $C$, thus, $\angle B = 16.5^\circ$ So, angle $B = 16.5^\circ$.

Would you like more details or have any questions?

Here are some related questions you might consider asking:

1. How do you find the exterior angle of a triangle?
2. What is the sum of the exterior angles of any polygon?
3. How do you calculate the area of a triangle given its angles and one side?
4. How do you use the sine rule in non-right triangles?
5. What are the properties of cyclic quadrilaterals?

Tip: When solving for angles in a triangle, remember that the sum of the interior angles is always 180°. This property is fundamental and helps to quickly find unknown angles when two angles are given.