Question

circle d is shown in the diagram below. ∠abc has measure (3x + 2)° and ∠adc has measure (5x + 24)°. solve for x. x =

Explanation:

Step1: Recall the central angle theorem

The central angle theorem states that the measure of a central angle is twice the measure of the inscribed angle subtended by the same arc. So, \( \angle ADC = 2\angle ABC \).

Step2: Substitute the given expressions

We know \( \angle ABC=(3x + 2)^\circ \) and \( \angle ADC=(5x + 24)^\circ \). Substituting into the theorem: \( 5x + 24 = 2(3x + 2) \).

Step3: Expand and solve the equation

Expand the right - hand side: \( 5x+24 = 6x + 4 \).
Subtract \( 5x \) from both sides: \( 24=x + 4 \).
Subtract 4 from both sides: \( x=24 - 4=20 \).

Answer:

\( x = 20 \)