2003 - WAEC Mathematics Past Questions and Answers - page 3

Sum of interior angles in a quadrilateral is 360
(x + 20)^o + (x+ 10)^o + (2x - 45)^o + (x - 25)^o = 360^o
5x^o - 40^o = 360^o
x = 400/5 = 80^o

Sum of interior angle of the diagram equals 360^o
180^o - 5y^o + 136^o + 180^o + 180^o - 3y^o = 360^o
-8y^o + 136^o = 0
-8y^o = -136; y = 17

Member that are neither doctors nor lawyers = 60-(15+9)=36
Probability (Not doctors ad not lawyers) (=\frac{36}{60}<br /> =\frac{6}{10}=\frac{3}{5})

The fraction is undefined when the denominator is equal to zero
(2x^2 - 13x + 15 = 0<br /> 2x^2 - 3x - 10x + 15<br /> x(2x-3)-5(2x-3) = 0<br /> (2x-3)(x-5)=0<br /> x = \frac{3}{2} or x = 5)

< QPS = < PRS = 65° (angles in the same segment)

< PSR + 40° + 65° = 180°

< PSR + 105° = 180°

< PSR = 75°

< PSR = < PSQ + < QSR

75° = < PSQ + 20° \(\implies\) < PSQ = 75° - 20° = 55°

\((111_{2})^2 - (101_{2})^2\)

Difference of two squares

\((111 - 101)(111 + 101)\)

= \((10)(1100)\)

= \(11000_{2}\)

(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}<br /> 3^{1-n}\times 3^{-2(-2n)} = 3^{-2}<br /> 1-n-2(-2n)= -2<br /> 1-n+4n=-2<br /> n=-1)

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have

\((n - 2) \times 180° = 108n\) ... (1)

\((n - 2) \times 180° = 116n\) ... (2)

\((n - 2) \times 180° = 120n\) ... (3)

Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.

(1): \(180n - 360 = 108n \implies 72n = 360\)

 \(n = 5\) (regular pentagon)

(2): \(180n - 360 = 116n \implies 64n = 360\)

 \(n = 5.625\)

(3): \(180n - 360 = 120n \implies 60n = 360\)

 \(n = 6\) (regular hexagon)

Hence, 116° is not an angle of a regular polygon.

(sin \theta = \frac{opp}{hyp}<br /> sin 60^o = \frac{|YZ|}{|XZ|}=\frac{6}{P}<br /> P sin 60^o = 6<br /> P = \frac{6}{sin60^o}<br /> =\frac{6}{\sqrt{\frac{3}{2}}}=4\sqrt{3})