1.1 Angles and Lines II

Posted on December 1, 2017 by user

1.1 Angles and Lines II

Identifying Parallel, Transversals, Corresponding Angles, Alternate Angles and Interior Angles

(A) Parallel lines

Parallel lines are lines with the same direction. They remain the same distance apart and never meet.

(B) Transversal lines

A transversal is a straight line that intersects two or more straight lines.

(C) Alternate angles

(D) Corresponding angles

(E) Interior angles

PT3 Smart TIP

Alternate angles are easily identified by tracing out the pattern “Z” as shown.

Corresponding angles are easily identified by the pattern “F” as shown.

Interior angles are easily identified by the pattern “C” as shown.

Example 1:

In Diagram below,PQ is parallel to RS. Determine the value of y.

Solution:

Construct a line parallel to PQ and passing through W.

a = 40^o and b = 50^o← (Alternate angles)

y = a + b

= 40^o+ 50^o

= 90^o

Example 2:

In Diagram below, PSQ and STU are straight lines. Find the value of x.

Solution:

\begin{array}{l} ∠ W S Q = 180^{o} - 150^{o} \\ = 30^{o} \leftarrow Supplementary angle \\ ∠ X T U = ∠ W S Q + ∠ x \leftarrow Corresponding angle \\ 75^{o} = 30^{o} + ∠ x \\ ∠ x = 75^{o} - 30^{o} \\ ∠ x = 45^{o} \\ x = 45 \end{array}