Find the Measure of BTopic: Inscribed Angles and Central Angles
1 answer:
Answer:
Option B
The measure of angle b is 75°
Step-by-step explanation:
Method 1
we know that
In a inscribed quadrilateral, the opposite angles are supplementary
so
∠a+60°=180° ------> equation A
∠b+105°=180° -----> equation B
To find the measure of angle b solve the equation B
∠b+105°=180°
Subtract 105° both sides
∠b+105°-105°=180°-105°
∠b=75°
Method 2
see the attached figure with letters to better understand the problem
we know that
The inscribed angle measures half that of the arc comprising
so
∠105°=(1/2)[arc ADC]
arc ADC=2*105°=210°
<em><u>Find the measure of arc ABC</u></em>
we know that
arc ABC+arc ADC=360° -----> by complete circle
arc ABC=360°-210°=150°
<u><em>Find the measure of inscribed angle b</em></u>
∠b=(1/2)[arc ABC]
substitute
∠b=(1/2)[arc 150°]=75°
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Step-by-step explanation:
The simplification form of the provided expression is x¹⁸a³b³ option
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<h3>What is an integer exponent?</h3>In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The expression:
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= a³b³x¹⁸ Or
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(d) x¹⁸a³b³ is correct.
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