Question

module 15 quiz - a
write your answers on the lines provided.
use the circle to the left for questions 1 and 2

1. find the ( mangle bca ) if arc ( ab = 150^circ ).

( mangle bca = )

1. find the measure of arc ( be ) if ( mangle bae = 42^circ ).

arc ( be = )
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Explanation:

Question 1

Step1: Identify the central angle

The measure of a central angle is equal to the measure of its intercepted arc. Here, $\angle BCA$ is a central angle intercepting arc $AB$.

Step2: Determine the measure

Given arc $AB = 150^\circ$, so $m\angle BCA = 150^\circ$ (since central angle = measure of its arc).

Step1: Recall the inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle BAE$ is an inscribed angle intercepting arc $BE$.

Step2: Calculate the arc measure

Let the measure of arc $BE$ be $x$. By the inscribed angle theorem, $m\angle BAE=\frac{1}{2}x$. Given $m\angle BAE = 42^\circ$, we solve for $x$:
$$42^\circ=\frac{1}{2}x$$
Multiply both sides by 2: $x = 2\times42^\circ = 84^\circ$.

Answer:

$150^\circ$

Question 2