Exercise 1 Page 799

If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent. Note in the diagram below that ∠ B and ∠ C both intersept AD. So, ∠ B ≅ ∠ C.

We can see that ∠ E and ∠ F are inscribed angles that intercept the same arc.

Since both inscribed angles in our diagram intercept the same arc, they are congruent. This means, they have the same measure. ∠ E ≅ ∠ F ⇕ m∠ E= m∠ F Let's substitute m∠ E for 6x+2 and m∠ F for 3x+23 and solve for x.

m∠ E= m∠ F

SubstituteII

m∠ E= 6x+2, m∠ F= 3x +23

6x+2= 3x+23

▼

SubEqn

LHS-3x=RHS-3x

3x+2=23

SubEqn

LHS-2=RHS-2

3x=21

DivEqn

.LHS /3.=.RHS /3.

x=7

Therefore, the value of x is 7. This corresponds to option D.