What is the value of x ? explain ( chords and arcs )

x ≈ 9.4

Step-by-step explanation:

The segment from the centre is a perpendicular bisector of the chord.

Using Pythagoras' identity in the right triangle formed with hypotenuse 13 and legs 9 and x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 9² = 13²

x² + 81 = 169 ( subtract 81 from both sides )

x² = 88 ( take the square root of both sides )

x = = 2 ≈ 9.4 ( to 1 dec. place )

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.