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^\circ. Find < QRS.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) x < 4 or -1 \(\geq\) x. The range of values of x is -1 \(\geq\) x < 4.
(b) First, < PQR + 56^\circ= 180^\circ
so that < PQR = 180^\circ- 56^\circ= 124^\circ From triangle PQR,
< PQR + < QRP+ < QPR = 180^\circ. But IRQI = IQPI
so that < QRP = < QPR.
124^\circ + 2 < QRP = 180^\circ and < QRP =28^\circ.
But < PRS = 90^\circ (angle on a semi-circle), therefore, < QRS = 28^\circ+ 90^\circ = 118^\circ.
Source: Myschool Past Questions Archive (Record #56329)