Angle MeasuresLT – I can find and compare angle measures.

The name can be the vertex of the angle: / G.

The name can be three points that include on each ray with the vertex written in the middle/ AGC, / CGA.

The name can be the number between the sides of the angle: / 3.

Angle – formed by two rays with the same endpoint. The rays are the sides or legs of the angle and the endpoint is the vertex.

vertex

A. Naming an Angle

Definition of an Angle

Example 1: Name all the angles

/ 1

/ ABC / F

Example 2: Name the Adjacent Angles

/ POR &

/ ROQ

NOT / ORQ ,/ ORP,

or /O

These angles are called “adjacent” which means “next to” because they share a ray.

B. Classifying Angles

Acute < 90

Obtuse > 90

Right = 90

Straight = 180

State whether the following are acute, right, or obtuse.

1.

2.

3.

4.

5.

??

acute

obtuse

right

obtuseacute

m /1 + m /2 = m/ ABC Angle Addition Postulate.

42 + m/2 = 88 Substitute 42 for m/1 and 88 for m/ABC.

m/2 = 46 Subtract 42 from each side.

Example 1 Suppose that m/1 = 42 and m/ ABC = 88. Find m/2.

C. Angle Addition Postulate

42°

88°

Example 2 If m/RQT = 155, what are m/RQS and m/TQS?

(4x – 20) + (3x + 16) = 155 7x – 6 = 155 Combine like terms. 7x = 161 Add 6 to each side x = 23 Divide each side by 7.

m/RQS = 4x – 20 = 4(23) – 2 0 = 92 – 20 = 72

m/TQS = 3x + 14 = 3(23) + 14 = 69 + 14 = 83

D. Congruent AnglesAngles with the same measure are congruent. Congruent angles are marked by arcs.

For example …

/CBJ /DHG

If m /GHF = 130, then, m /JBC = 130

130°130°

When we use a protractor, we need to line it up correctly.

You need to make sure the protractor is lined up correctly.

Is this ready to measure the angle?

Were you right......................it wasn’t

Look for the upside down ‘T’ in the middle of the straight line on your protractor.

This needs to be exactly on the vertex of your angle.

We need to remember.....

It doesn’t matter which way round the angle is, you ALWAYS need to line the upsidedown ‘T’ to the vertexof the angle.

Now you are ready.

Read from the 0°, and follow the inner set of numbers.

Once you reach 30° you need to be careful!!!

You then need to look at the 1° markings on the outer set of numbers.

What does it measure?

This angle measures 35°.