Theory question 107
Angles and Polygons(a) In the diagram below, BA is parallel to DE. Find the value of x.
(b) Illustrate graphically and shade the region in which the inequalities y − 2x < 5, 2y + x ≥ 4
Show the model answer
(a) The interior angle at D is 360° − 312° = 48°.
Draw a line through C parallel to BA and DE: it splits ∠BCD into 52° (alternate to ∠ABC) and 48° (alternate to the 48° at D), so ∠BCD = 100°.
x is the reflex angle at C: x = 360° − 100° = 260°
(b) Draw y − 2x = 5 as a broken line (through (0, 5) and (−2.5, 0)) and x + 2y = 4 as a solid line (through (0, 2) and (4, 0)).
The required region is below y = 2x + 5 and on or above x + 2y = 4 (it contains e.g. (2, 2)); the lines meet at (−1.2, 2.6). Shade (or leave unshaded, as instructed) and label the region.
Through the bend point, draw a line parallel to the two parallel lines and use alternate angles.