Calculate degree of angles in plane figures (triangle, rectangle and circle)

A triangle has three interior angles. The sum of these three angles is always 180°.

To find a missing angle in a triangle: $Missing\ angle = 180° - (Angle\ 1 + Angle\ 2)$

Example: In a triangle, two angles measure 60° and 70°. Find the third angle.

Solution: $Third\ angle = 180° - (60° + 70°)$ $Third\ angle = 180° - 130°$ $Third\ angle = 50°$

A rectangle is a quadrilateral with four right angles. Each interior angle of a rectangle measures 90°. The sum of all four angles is: $90° + 90° + 90° + 90° = 360°$

Example: A rectangular piece of land in a village has three angles measuring 90° each. What is the measure of the fourth angle?

Solution: $Fourth\ angle = 360° - (90° + 90° + 90°)$ $Fourth\ angle = 360° - 270°$ $Fourth\ angle = 90°$

A complete circle contains 360°. This means if you walk all the way around a circular path, you have turned through 360°. Parts of a circle can also be measured as fractions of 360°.

Example: A circular market bazaar is divided into 4 equal sections. What is the angle of each section?

Solution: $Angle\ of\ each\ section = \frac{360°}{4} = 90°$

When you need to measure an angle directly, use a protractor:

1. Place the protractor's center hole on the vertex (corner point) of the angle
2. Align the baseline of the protractor with one arm of the angle
3. Read the degree where the other arm crosses the scale
4. Use the inner scale if measuring from right to left, or outer scale if measuring from left to right

Example: Measure the angle shown where two roads meet.

• Place protractor center at the intersection
• Align baseline with one road
• Read the degree on the scale where the other road points
• This gives you the angle in degrees

When a farmer in Tanzania wants to divide a circular shamba (plot) into equal sections for planting different crops, he needs to know that a circle has 360°. If he divides it into 6 equal parts, each part will have $360° ÷ 6 = 60°$. This same knowledge is used by builders when laying out rectangular rooms, ensuring all corners are 90° for proper construction.