Question

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

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

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

Answer 2

Applying the intersecting chords theorem, the measure of ∠WXS is: 2. 60°

What is the Intersecting Chords Theorem?

When two chords of a circle intersect each other, the measure of the vertical angle formed equals half of the sum of the intercepted arcs, based on the intersecting chords theorem.

Given the following measures:

• m(SW) = 38°
• m(WR) = 98°

m(RT) = 180 - m(WR) (semicircle = 180°)

m(RT) = 180 - 98

m(RT) = 82°

m∠WXS = 1/2[m(RT) + m(SW)] (intersecting chords theorem)

m∠WXS = 1/2(82 + 38)

m∠WXS = 60°

Learn more about the intersecting chords theorem on:

https://brainly.com/question/13950364