8.1.3 Lines and Angles (Sample Questions) - Mathematics

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{matrix} ∠ 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{matrix}

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

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