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Essay On Lines And Angles Worksheet

Angles Worksheets – Angle worksheets cover almost all aspects of angle topics in geometry. It contains naming angles in different ways, identifying parts of the angles, classifying types, measuring angles with protractor, complementary and supplementary angles, angles formed between intersecting lines, simple algebra problems based on angles, angles formed by parallel lines and a transversal and more. It also contains angle worksheets based on geometric shapes such as triangle, quadrilateral, polygon and more.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

CCSS.Math.Content.4.G.A.1 – Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

CCSS.Math.Content.4.G.A.2 – Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Geometric measurement: understand concepts of angle and measure angles.

CCSS.Math.Content.4.MD.C.5 – Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

CCSS.Math.Content.4.MD.C.5.a  – An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

CCSS.Math.Content.4.MD.C.5.b – An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

CCSS.Math.Content.4.MD.C.6  – Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

CCSS.Math.Content.4.MD.C.7  – Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

CCSS.MATH.CONTENT.7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

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Types of Angle Pairs

Adjacent angles: two angles with a common vertex, sharing a common side and no overlap.

Angles ∠1 and ∠2 are adjacent.

Complementary angles: two angles, the sum of whose measures is 90°.

Angles ∠1 and ∠2 are complementary.

Complementary are these angles too(their sum is 90°):

Supplementary angles: two angles, the sum of whose measures is 180°.

Angles ∠1 and ∠2 are supplementary.

Angle pairs formed by parallel lines cut by a transversal

When two parallel lines are given in a figure, there are two main areas: the interior and the exterior.

When two parallel lines are cut by a third line, the third line is called the transversal. In the example below, eight angles are formed when parallel lines m and n are cut by a transversal line, t.

There are several special pairs of angles formed from this figure. Some pairs have already been reviewed:
Vertical pairs:
∠1 and ∠4
∠2 and ∠3
∠5 and ∠8
∠6 and ∠7
Recall that all pairs of vertical angles are congruent.
Supplementary pairs:
∠1 and ∠2
∠2 and ∠4
∠3 and ∠4
∠1 and ∠3
∠5 and ∠6
∠6 and ∠8
∠7 and ∠8
∠5 and ∠7
Recall that supplementary angles are angles whose angle measure adds up to 180°. All of these supplementary pairs are linear pairs. There are other supplementary pairs described in the shortcut later in this section. There are three other special pairs of angles. These pairs are congruent pairs.

Alternate interior angles two angles in the interior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate interior angles are non-adjacent and congruent.


Alternate exterior angles two angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent.


Corresponding angles two angles, one in the interior and one in the exterior, that are on the same side of the transversal. Corresponding angles are non-adjacent and congruent.

Use the following diagram of parallel lines cut by a transversal to answer the example problems.

Example:
What is the measure of ∠8?
The angle marked with measure 53° and ∠8 are alternate exterior angles. They are in the exterior, on opposite sides of the transversal. Because they are congruent, the measure of ∠8 = 53°.
Example:
What is the measure of ∠7?
∠8 and ∠7 are a linear pair; they are supplementary. Their measures add up to 180°. Therefore, ∠7 = 180° – 53° = 127°.

1. When a transversal cuts parallel lines, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent.

In the figure above ∠1, ∠4, ∠5, and ∠7 are all acute angles. They are all congruent to each other. ∠1 ≅ ∠4 are vertical angles. ∠4 ≅ ∠5 are alternate interior angles, and ∠5 ≅ ∠7 are vertical angles. The same reasoning applies to the obtuse angles in the figure: ∠2, ∠3, ∠6, and ∠8 are all congruent to each other.

2. When parallel lines are cut by a transversal line, any one acute angle formed and any one obtuse angle formed are supplementary.

From the figure, you can see that ∠3 and ∠4 are supplementary because they are a linear pair.
Notice also that ∠3 ≅ ∠7, since they are corresponding angles. Therefore, you can substitute ∠7 for ∠3 and know that ∠7 and ∠4 are supplementary.

Example:
In the following figure, there are two parallel lines cut by a transversal. Which marked angle is supplementary to ∠1?

The angle supplementary to ∠1 is ∠6. ∠1 is an obtuse angle, and any one acute angle, paired with any obtuse angle are supplementary angles. This is the only angle marked that is acute.

Other resources:

Angles - Problems with Solutions
Types of angles
Parallel lines cut by a transversal Test

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