Question

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

Answer 1

The measure of angles of △SPT are

∠PTS=35°, ∠PST=19°, ∠SPT=126°

Explanation:

Given the figure in which

m∠EPT=54° and arc TP=70°

we have to find angles of △SPT

By tangent chord angle theorem, which states that the angle make by a tangent to a circle and a chord is equals to half of the angle measure of the intercepted arc i.e

`\angle PTS=(1)/(2)\angle POT`

`\angle PTS=(1)/(2)* 70^(\circ)=35^(\circ)`

As ∠EPT and ∠SPT form linear pair therefore their sum equals to 180°

⇒ ∠EPT+∠SPT=180°

54°+∠SPT=180°

∠SPT=126°

In △SPT, by angle sum property of triangle

∠PST+∠SPT+∠PTS=180°

∠PST+126°+35°=180°

∠PST=19°