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
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
Sum of exterior angles = 360°
2x + 3x + 2x + 3x + 5x = 360°
15x = 360°
x = 360°/15 = 24°
In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ∠SRQ = 75°, ∠QPT = 25° and PQR is straight line. Find ∠RST
< 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°
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° ?
\(\cos \theta = \frac{5}{13}\)
\(\implies\) 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