Question

Arc QVT measures 156. Which statement must be true?

Answer 1

A.) QRT and QST both measure 78 degrees

Explanation:

I used process of elimination for this they had to be the same and the both aren't obtuse

Answer 2

∠QRT and ∠QST both angles have measure 78°

Explanation:

Given the figure in which measure of arc QVT is 156°

we have to choose the correct statement.

As given arc QVT=156° i.e ∠QPT=156°

By theorem angle made by same arc i.e inscribed angle formed by same arc are equal.

⇒ ∠QRT=∠QST

Also another theorem angle subtended at the centre is twice the angle at the circumference

⇒ ∠QPT=2∠QRT=2∠QST

`2\angle QRT=\angle QPT=156^(\circ)`

`\angle QRT=(156)/(2)=78^(\circ)`

⇒ ∠QRT and ∠QST both angles have measure 78°

Hence, option 1 is correct.