Question

What is the measure of angle ABC? • 36° • 43° • 72° • 144°

Answer 1

Given that the measure of ∠ADC = (7x + 2)° and arc AC = (8x - 8)°

We need to determine the measure of ∠ABC

The value of x:

The measure of ∠ADC can be determined using the formula,

$m\angle ADC=m \widehat{AC}$

Substituting the values, we get;

$7x+2=8x-8$

$-x+2=-8$

     $-x=-10$

       $x=10$

Thus, the value of x is 10.

The measure of ∠ADC:

Substituting the value x = 10 in the measure of ∠ADC = (7x + 2)°

We have;

$\angle ADC=(7(10)+2)^{\circ}$

$\angle ADC=(70+2)^{\circ}$

$\angle ADC=72^{\circ}$

Thus, the measure of ∠ADC is 72°

The measure of ∠ABC:

The measure of ∠ABC can be determined using the central angle theorem.

Thus, we have;

$\angle ADC=2\angle ABC$

     $72^{\circ}=2\angle ABC$

     $36^{\circ}=\angle ABC$

Thus, the measure of ∠ABC is 36°

Hence, Option A is the correct answer.

Answer 2

Answer:

A

Step-by-step explanation: I just took the test