# Question Video: Finding the Measure of an Angle given Its Arcβs Measure Using Another Inscribed Angle Mathematics

Given that πβ π΄π΅πΆ = 30.5Β°, find πβ π΅π·πΆ.

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### Video Transcript

Given that the measure of angle π΄π΅πΆ is equal to 30.5 degrees, find the measure of angle π΅π·πΆ.

So the first thing we can do to start to solve this problem is how we look at our angle π΄π΅πΆ. Well, we know that the measure of an inscribed angle is half the measure of that that subtends it. So what does this mean in practice? It means that the angle π΄π΅πΆ is half of the angle that is at the arc πΆπ΄.

So therefore, we can say that the measure of angle π΄π΅πΆ is equal to half the measure of the arc πΆπ΄. And as we know that the measure of angle π΄π΅πΆ is equal to 30.5, we can say that 30.5 is equal to half the measure of the arc πΆπ΄. So therefore, if we multiply each side of the equation by two, we can get that the measure of the arc πΆπ΄ is gonna be equal to 61 degrees.

But how does this help us? Well, first of all, weβre gonna look at another relationship. We can see that π΄π΅, through the line π΄π΅, passes through π, which is the centre of our circle. So therefore, the arc π΄ to π΅ must be equal to 180 degrees. So therefore, we can say that the measure of the arc from πΆπ΄π΅ is gonna be equal to the measure of the arc πΆπ΄ plus 180 because itβd be plus the arc π΄ to π΅. So therefore, we can say that the measure of the arc from πΆπ΄π΅ is gonna be equal to 241 degrees cause itβs 61 plus 180.

Well now, if we take a look back at the question, what we want to do is find the measure of the angle π΅π·πΆ. Well, if we look at π΅π·πΆ, then the angle π΅π·πΆ is actually subtended by the arc πΆπ΄π΅. So therefore, we can say that the measure of the angle π΅π·πΆ is gonna be equal to half of the arc πΆπ΄π΅. So therefore, we can say that the measure of angle π΅π·πΆ is gonna be equal to a half multiplied by 241.

So therefore, we can say that the measure of angle π΅π·πΆ is gonna be equal to 120.5 degrees. Itβs cause that was half of 241.