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VMariaS [17]
2 years ago
14

Given: mTP= 70°,m∠EPT = 54° Find: Angles of △SPT

Mathematics
1 answer:
Zigmanuir [339]2 years ago
5 0

Answer:

The Angles of △SPT are

m\angle STP=35\°  

m\angle SPT=126\°

m\angle PST=19\°

Step-by-step explanation:

step 1

Find the measure of angle PET

we know that

The inscribed angle is half that of the arc it comprises.

m\angle PET=\frac{1}{2}(arc\ PT)

substitute the given values

m\angle PET=\frac{1}{2}(70\°)

m\angle PET=35\°

step 2

Find the measure of angle PTE

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle PET

m\angle PET+m\angle EPT+m\angle PTE=180\°

substitute the given values

35\°+54\°+m\angle PTE=180\°

m\angle PTE=180\°-89\°=91\°

step 3

Find the measure of angle STP  

we know that

The inscribed angle is half that of the arc it comprises.

m\angle STP=\frac{1}{2}(arc\ TP)

substitute the given values

m\angle STP=\frac{1}{2}(70\°)=35\°

step 4

Find the measure of angle SPT

we know that

m\angle SPT+m\angle EPT=180\° ----> by supplementary angles

m\angle SPT+54\°=180\°

m\angle SPT=180\°-54\°=126\°

step 5

Find the measure of angle PST

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle SPT

m\angle STP+m\angle SPT+m\angle PST=180\°

substitute the given values

35\°+126\°+m\angle PST=180\°

m\angle PST=180\°-161\°=19\°

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