1.2.2 Angles and Lines II, PT3 Practice

Question 6:
In Diagram below, PQRST is a straight line. Find the value of x.

Solution:
$\begin{array}{l}\text{Interior angle of }R=\left({180}^o-{76}^o\right)÷2={52}^o\\ \angle x=\text{exterior angle of }R\left(\text{corresponding angles}\right)\\ \text{Hence, }x={76}^o+{52}^o={128}^o\end{array}$

Question 7:
In Diagram below, find the value of y.



Solution:


$\begin{array}{l}\angle ABC=\angle BCD\\ ={108}^o\text{ (alternate angle)}\\ y^o+{130}^o+{108}^o={360}^o\\ y^o={360}^o-{238}^o\\ y^o={122}^o\end{array}$

Question 8:
In Diagram below, PSR and QST are straight lines.
Find the value of x.

Solution:
$\begin{array}{l}\angle UST+\angle STV={180}^o\\ \angle UST={180}^o-{116}^o={64}^o\\ \angle PST=\angle QSR\\ x^o+\angle UST={135}^o\\ x^o+\angle UST={135}^o\\ x^o={71}^o\\ x=71\end{array}$

Question 9:
In Diagram below, PWV is a straight line.

(a) Which line is perpendicular to line PWV?
(b) State the value of  ∠ RWU.

Solution:
(a) SW

(b) ∠ RWU = 13^o + 29^o + 20^o = 62^o

 

Question 10:
In Diagram below, UVW is a straight line.


(a) Which line is parallel to line TU?
(b) State the value of  ∠ QVS.

Solution:
(a) QV

(b) ∠ QVS = 8^o + 18^o = 26^o