Question

Given the angles inscribed in the circle, find m ∠ DBC.

Answer 1

Answer:

m∠DBC = 51°

Step-by-step explanation:

Circle Theorem vocabulary

• Chord: A straight line joining two points on the circle.
• Inscribed angle: The angle formed when two chords meet at one point on a circle.
• Intercepted arc: The arc that is between the endpoints of the chords that form the inscribed angle.

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore:

$\sf \implies \angle DBC=\dfrac{1}{2}\:\overset{\frown}{BC}$

$\sf \implies \angle DBC=\dfrac{1}{2}\:(102^{\circ})$

$\sf \implies \angle DBC=51^{\circ}$

Learn more about the Inscribed Angle Theorem here:

brainly.com/question/27934538

brainly.com/question/27943630

Answer 2

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

To determine ∠DBC, we will apply the theorem relating the inscribed angle to the intercepted arc:

$\longrightarrow \sf{Intercepted \: arc= (inscribe \: angle)}$

$\longrightarrow \sf{Intercept \: arc= 102^\circ}$

$\longrightarrow \sf{Inscribed \: angle= \angle DBC }$

$\longrightarrow \sf{102=2( \angle DBC)}$

$\longrightarrow \sf{\angle DBC= \dfrac{102}{2} }$

▪ $\longrightarrow \sf{\angle DBC = 51^\circ}$

$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

$\boxed{\bf{\large m \: \angle DBC= 51^\circ}}$