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In figure at the right, quadrilateral LOST is inscribed in OU, if m<LTS = 81° and m<TSO = 96°, find the measure of the following:​​

In Figure At The Right Quadrilateral LOST Is Inscribed In OU If MltLTS 81 And MltTSO 96 Find The Measure Of The Following class=

Sagot :

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Answer:

1. m∠TLO = 84°

Solution:

The sum of the measure of the opposite angles of the quadrilateral are supplementary angles, which equals 180°.

If ∠TSO = 96°, then we must find the measure of ∠TLO.

∠TSO + ∠TLO = 180°

96 + ∠TLO = 180

∠TLO = 180 - 96

∠TLO = 84°

2. M∠LOS = 99°

Solution:

The sum of the measure of the opposite angles of the quadrilateral are supplementary angles, which equals 180°.

If ∠LTS = 81°, then we must find the measure of ∠LOS.

∠LTS + ∠LOS = 180°

81 + ∠LOS = 180°

∠LOS = 180 - 81

∠LOS = 99°

3. Measure of arc LTS = 198

Solution:

If ∠LOS = 99, then arc LTS is doubled the measure of ∠LOS.

Arc LTS =  2 ∠LOS

Arc LTS = 2 ( 99)

Arc LTS = 198°

4. Measure of Arc TSO = 168°

Solution:

If ∠TLO = 84°, then Arc TSO is doubled to the measure of ∠TLO.

Arc TSO = 2 ∠TLO

Arc TSO = 2 (84)

Arc TSO = 168°

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