a. Find the range of values of x which satisfy the following inequalities simultaneously: 5 – x > 1 and 9 + x \(\geq\) 8
In the diagram, O is the centre of the circle, IPQI = IQRI and < PSR = 56°. Find < QRS.
Explanation
(a) x < 4 or -1 \(\geq\) x. The range of values of x is -1 \(\geq\) x < 4.
(b) First, < PQR + 56°= 180°
so that < PQR = 180°- 56°= 124° From triangle PQR,
< PQR + < QRP+ < QPR = 180°. But IRQI = IQPI
so that < QRP = < QPR.
124° + 2 < QRP = 180° and < QRP =28°.
But < PRS = 90° (angle on a semi-circle), therefore, < QRS = 28°+ 90° = 118°.