Question

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

Answer 1

The Angles of △SPT are

`m\angle STP=35\°`

`m\angle SPT=126\°`

`m\angle PST=19\°`

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=(1)/(2)(arc\ PT)`

substitute the given values

`m\angle PET=(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=(1)/(2)(arc\ TP)`

substitute the given values

`m\angle STP=(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\°`