https://file.aiquickdraw.com/mathbot/file/17218471377851retyk69.png

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.

Learn how to calculate missing angles in triangles and circles with detailed step-by-step solutions. Covering the Triangle Angle Sum Theorem and circle angle properties, this problem-solving guide is suitable for students in Grades 7-9.

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