Question Video: Finding the Measure of an Angle given Its Arc’s Measure Using Another Inscribed Angle by Solving Two Linear Equations | Nagwa Question Video: Finding the Measure of an Angle given Its Arc’s Measure Using Another Inscribed Angle by Solving Two Linear Equations | Nagwa

Question Video: Finding the Measure of an Angle given Its Arcβs Measure Using Another Inscribed Angle by Solving Two Linear Equations Mathematics • Third Year of Preparatory School

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Given that πβ π΄πΈπΆ = 36Β° and πβ π΅π΄π· = (4π₯ β 8)Β°, determine the value of π₯.

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Video Transcript

Given that the measure of angle π΄πΈπΆ equals 36 degrees and the measure of angle π΅π΄π· equals four π₯ minus eight degrees, determine the value of π₯.

We are given, firstly, that the measure of angle π΄πΈπΆ is 36 degrees. The measure of angle π΅π΄π· is four π₯ minus eight degrees. We donβt have any theorems that tell us immediately how these two angles are related. So letβs observe that we are given a set of parallel line segments. The line segment π΄π΅ is parallel to the line segment πΆπ·. And so we can say that this angle of π΄π·πΆ must be alternate to angle π΅π΄π·. So they will have equal angle measures of four π₯ minus eight degrees.

Now, we can use the property that inscribed angles subtended by the same arc are equal. We should observe that this arc π΄πΆ subtends two angles, angle π΄π·πΆ and angle π΄πΈπΆ, meaning that these two angle measures will be the same. And so we can set up an equation that four π₯ minus eight degrees is equal to 36 degrees. Since the brackets on the left-hand side are simply there just to indicate that this is a measure in angles, then we can drop the brackets and the degrees from both sides of the equation. We can then add eight to both sides, giving us four π₯ is equal to 44. Dividing both sides of the equation, we have the answer that π₯ is equal to 11.

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