In the diagram above, O is the centre of a circle NST. |NT| = |ST| and ∠NTS = 36°. Find the measure of the angle marked t.

gigiisnothere

1 year ago

ITS ACTUALLY OPTION D



∣NT∣=∣ST∣ (this means triangle NTS is isosceles).

∠𝑁𝑇𝑆=36∘
We need to find the angle marked 𝑡
Step 1: Find∠𝑇𝑁𝑆. Since triangle NTS is isosceles, the two base angles are equal:
∠𝑇𝑁𝑆=∠𝑁𝑇𝑆=36 ∘

Step 2: Find the Angle at the Centre (O)
The angle at the centre subtended by the chord NS (which is ∠𝑁𝑂𝑇 is twice the angle at the circumference (
∠𝑁𝑇𝑆 due to the angle at the centre theorem:
∠𝑁𝑂𝑆=2×36∘=72∘ ..
∘

Step 3: Find Angle 𝑡. Since 𝑡 t is the exterior angle of triangle OST, we use the exterior angle theorem:
𝑡=180∘−∠𝑁𝑂𝑆
=108