Question

name:____ date:__ period:____
classifying angles:
measuring angles: provide the measure of: <ghl:____ <khl:__ <jhk:__ <mhl:__ <ghk:__ <ghj:____
naming angles: provide three names for the following angle: give two more names for angles: <1: <2:
congruent angles: find the value of x if <lkm = <mkn: find the length of x if the angles are congruent.

Explanation:

Classifying Angles:

Acute Angle:

An angle less than 90 degrees.

Right Angle:

An angle equal to 90 degrees.

Obtuse Angle:

An angle between 90 and 180 degrees.

Straight Angle:

An angle equal to 180 degrees.

Reflex Angle:

An angle between 180 and 360 degrees.

Full - turn Angle:

An angle equal to 360 degrees.

Measuring Angles (assuming protractor - based measurement):

For ∠GHL:

Align protractor, read value.

For ∠KHL:

Align protractor, read value.

For ∠JHK:

Align protractor, read value.

For ∠MHL:

Align protractor, read value.

For ∠GHK:

Align protractor, read value.

For ∠GHJ:

Align protractor, read value.

Naming Angles:

For the first angle:

∠1 can be named as ∠ABC, ∠CBA, ∠B.

For the second set of angles:

For ∠1: ∠SKY, ∠YKS.
For ∠2: ∠YKL, ∠LKY.

Congruent Angles:

First congruent - angle problem:

If ∠LKM = ∠MKN, then 2x + 10=4x - 11.

Step1: Rearrange terms

Subtract 2x from both sides: 10 = 4x-2x - 11, so 10 = 2x - 11.

Step2: Isolate x

Add 11 to both sides: 10 + 11=2x, 21 = 2x. Then x=\frac{21}{2}=10.5.

Second congruent - angle problem:

If the angles are congruent, 2x + 20=3x - 10.

Step1: Rearrange terms

Subtract 2x from both sides: 20 = 3x-2x - 10, so 20 = x - 10.

Step2: Isolate x

Add 10 to both sides: x=20 + 10=30.

Answer:

Classifying Angles:

(Answers depend on actual angle measures in the figures, but categories are acute, right, obtuse, straight, reflex, full - turn)

Measuring Angles:

(Answers depend on protractor measurements of given angles at H)

Naming Angles:

∠ABC, ∠CBA, ∠B; ∠SKY, ∠YKS; ∠YKL, ∠LKY

Congruent Angles:

x = 10.5; x = 30