Question

In circle K, diameter TW intersects chord RS at X such that mSW  38 and mWR 98 . Which of the

Answer 1

Answer:

$m\angle WXS=60^o$

Step-by-step explanation:

step 1

Find the measure of the arc RT

we know that

$arc\ WR+arc\ RT=180^o$ ----> because segment TW is a diameter

substitute the given values

$98^o+arc\ RT=180^o$

$arc\ RT=180^o-98^o=82^o$

step 2

we know that

The measure of the interior angle is the semi-sum of the arches that comprise it and its opposite

so

$m\angle WXS=\frac{1}{2}[arc\ SW+arc\ RT]$

substitute the values

$m\angle WXS=\frac{1}{2}[38^o+82^o]=60^o$