Home › Geometry - angles and clocks

Use the angle addition postulate in a proof

An interior ray splits an angle into two angles whose measures add

If ray $A C$ lies inside $∠ B A D$ , the angle addition postulate gives $m ∠ B A D = m ∠ B A C + m ∠ C A D$ . The interior-ray condition is essential.

Problem

Point $C$ lies in the interior of $∠ B A D$ . Given $m ∠ B A C = 2 0^{\circ}$ and $m ∠ C A D = 1 5^{\circ}$ , prove $m ∠ B A D = 3 5^{\circ}$ . Which reason justifies the equation $m ∠ B A D = m ∠ B A C + m ∠ C A D$ ?

Answer

The reason is the angle addition postulate. The whole angle measures

3 5^{\circ}

These angles do not need to form a straight line.

Step-by-step solution

1. Identify the two parts

Ray $A C$ lies inside $∠ B A D$ , dividing it into adjacent angles $∠ B A C$ and $∠ C A D$ .

2. State the reason

By the angle addition postulate,

m ∠ B A D = m ∠ B A C + m ∠ C A D .

3. Substitute the given measures

The sum is $2 0^{\circ} + 1 5^{\circ} = 3 5^{\circ}$ . This proves the required angle measure.

Add to Chrome - solve your own

Screenshot any problem on your screen and get the steps. Chrome on a computer; free.