Chapter 9.3, Problem 11WE

To determine

To complete: the given table.

Answer to Problem 11WE

$marcCB$	70	60	66	60	$p$
$marcBD$	30	28	$100-66=34$	$104-60=44$	$q$
$m\angle COD$	$70+30=100$	$60+28=88$	100	$2\cdot 52=104$	$p+q$
$m\angle CAD$	$\frac{1}{2}\cdot 100=50$	$\frac{1}{2}\cdot 88=44$	$\frac{1}{2}\cdot 100=50$	52	$\frac{1}{2}\cdot \left(p+q\right)$

Explanation of Solution

Given Information:

Given table,

$marcCB$	70	60	66	60	$p$
$marcBD$	30	28			$q$
$m\angle COD$			100
$m\angle CAD$				52

Calculation:

It shows a circle with points, $A,B,C$ and $D$ .

It is required to complete the table with the required values.

The measure of minor arc is same as the measure of its central angle and angle at the center of the circle is twice the angle at the circumference.

Based on the above rules and the filled in values given in the table, the final completed table will be,

$marcCB$	70	60	66	60	$p$
$marcBD$	30	28	$100-66=34$	$104-60=44$	$q$
$m\angle COD$	$70+30=100$	$60+28=88$	100	$2\cdot 52=104$	$p+q$
$m\angle CAD$	$\frac{1}{2}\cdot 100=50$	$\frac{1}{2}\cdot 88=44$	$\frac{1}{2}\cdot 100=50$	52	$\frac{1}{2}\cdot \left(p+q\right)$