8.2.3 Lines and Angles, PT3 Practice - Mathematics

Question 7:
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 8:
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

Question 9:

In Diagram below, find the value of x.

Solution:

40^o + 80^o + x^o+ x^o = 180^o

2x^o = 180^o – 120^o

2x^o = 60^o

x^o= 30^o

x = 30

Question 10:

In Diagram below, PQR is an isosceles triangle and QRS is a straight line.

Find the values of x and y.

Solution:

\begin{array}{l} ∠ P R Q = 180^{o} - 110^{o} = 70^{o} \\ ∠ P R Q = ∠ P Q R = 70^{o} \\ y^{o} = 180^{o} - 70^{o} - 70^{o} \\ = 40^{o} \\ y = 40 \\ x^{o} = 110^{o} - 40^{o} \\ = 70^{o} \\ x = 70 \end{array}

$\begin{array}{l} ∠ P R Q = 180^{o} - 110^{o} = 70^{o} \\ ∠ P R Q = ∠ P Q R = 70^{o} \\ y^{o} = 180^{o} - 70^{o} - 70^{o} \\ = 40^{o} \\ y = 40 \\ x^{o} = 110^{o} - 40^{o} \\ = 70^{o} \\ x = 70 \end{array}$

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