Question

(a) Find out the number of line segments in the following figure.

(b) Find the values of angles x, y and z in each of the following:


[4 MARKS]

Answer 1

(a) Correct answer: 1 Mark
(b) Each angle: 1 Mark


(a)

The total number of line segments is 8. The line segments are AF, AB, BF, FD, FC, CD, AC and BD.

(b) (i) Since $\angle A$ and $\angle {55}^{\circ }$ are vertically opposite,

$\angle x$ = ${55}^{\circ }$

$\angle x$ + $\angle z$ =${180}^{\circ }$

${55}^{\circ }$ + $\angle y$ = ${180}^{\circ }$

$\angle y$ = ${180}^{\circ }$ – ${55}^{\circ }$ = ${125}^{\circ }$

$\angle y$ = $\angle z$ (Vertically Opposite angles)

$\angle z$ = ${125}^{\circ }$


(ii) $\angle z$ = ${40}^{\circ }$ (Vertically opposite angles)

$\angle y$ + $\angle z$ = ${180}^{\circ }$

$\angle y$ = ${180}^{\circ }$ – ${40}^{\circ }$ = ${140}^{\circ }$

${40}^{\circ }$ + $\angle x$ + ${25}^{\circ }$ = ${180}^{\circ }$

${65}^{\circ }$ +$\angle x$ = ${180}^{\circ }$

$\angle x$ = ${180}^{\circ }$ – ${65}^{\circ }$ = ${115}^{\circ }$