Question

in circle d, angle adc measures $(7x + 2)^{circ}$. arc ac measures $(8x - 8)^{circ}$. what is the measure of $angle abc$?$\bigcirc$ $36^{circ}LXB0\bigcirc$ $72^{circ}$$\bigcirc$ $144^{circ}$

Explanation:

Step1: Relate central angle to arc

A central angle equals its intercepted arc.
$$7x + 2 = 8x - 8$$

Step2: Solve for $x$

Isolate $x$ by rearranging terms.
$$8 + 2 = 8x - 7x \implies x = 10$$

Step3: Find measure of arc $AC$

Substitute $x=10$ into arc formula.
$$8(10) - 8 = 80 - 8 = 72^\circ$$

Step4: Find inscribed angle $\angle ABC$

Inscribed angle is half its intercepted arc.
$$\angle ABC = \frac{1}{2} \times 72^\circ = 36^\circ$$

Answer:

36°