# 1992 - WAEC Mathematics Past Questions and Answers - page 3

In the diagram above, ML//PQ and NP//QR, if ∠LMN = 40° and ∠MNP = 55°. Find ∠QPR

^{o}

^{o}

^{o}

^{o}

**correct option:**a

Draw line ANB// ML

< MNA = 40° (alternate angle AB/ ML)

< ANP = 55° - 40° = 15°

< POR = 15° = < ANP (corresponding angles, PN // RQ)

The angles marked in the diagram above are measured in degrees. Find x

^{o}

^{o}

^{o}

^{o}

**correct option:**b

Sum of exterior angles = 360°

2x + 3x + 2x + 3x + 5x = 360°

15x = 360°

x = 360°/15 = 24°

^{o}. How many sides has the polygon

In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ∠SRQ = 75°, ∠QPT = 25° and PQR is straight line. Find ∠RST

^{o}

^{o}

^{o}

^{o}

**correct option:**c

< PTQ = 25° (base angles of an isos. triangle)

\(\therefore\) < PQT = 180° - (25° + 25°) = 130° (sum of angles in triangle PQT)

\(\therefore\) < RST = 130° - 75° = 55° (exterior angle = sum of 2 opp. interior angles)

Sin 60° has the same value as I. Sin 120° II. cos 240° III. -sin 150° IV. cos 210° V. sin 240°

**correct option:**a

In the second quadrant, \(\sin 120 = \sin (180 - 120)\)

= \(\sin 60\)

If cos θ = 5/13, what is the value of tan \(\theta\) for 0 < θ < 90° ?

**correct option:**d

\(\cos \theta = \frac{5}{13}\)

\(\implies\) In the right- angled triangle, with an angle \(\theta\), the adjacent side to \(\theta\) = 5 and the hypotenuse = 13.

\(\therefore 13^2 = opp^2 + 5^2\)

\(opp^2 = 169 - 25 = 144 \implies opp = \sqrt{144}\)

= 12.

\(\tan \theta = \frac{opp}{adj} = \frac{12}{5}\)

The value of tan 315°

The value of sin 210° is

^{o}from town Q while town R is south of town P and west of town Q. lf town R is 60km away from Q, how far is R from P?

**correct option:**d