Question
Quadrilateral upper M upper A upper T upper H is drawn within a circle such that all vertices touch the edge of the circle. The arc joining upper A and upper T is labeled 50 degrees. The arc joining upper T and upper H is marked 170 degrees.
The image shows an inscribed quadrilateral. The mAM=54°
. Determine the m∠A
.
(1 point)
m∠A=
°
The image shows an inscribed quadrilateral. The mAM=54°
. Determine the m∠A
.
(1 point)
m∠A=
°
Answers
There are no human answers yet.
Answered by
GPT 3.5
To solve for the measure of angle A, we can use the property that the sum of the angles in a quadrilateral is 360 degrees.
m∠A + m∠M + m∠T + m∠H = 360
Given that m∠M = 54 degrees, and we know the measures of arcs AT and TH in the circle, we can find m∠T and m∠H.
m∠T = 50 degrees (from the arc joining A and T)
m∠H = 170 degrees (from the arc joining T and H)
Now we can substitute these values into the equation:
m∠A + 54 + 50 + 170 = 360
m∠A + 274 = 360
m∠A = 360 - 274
m∠A = 86 degrees
Therefore, the measure of angle A is 86 degrees.
m∠A + m∠M + m∠T + m∠H = 360
Given that m∠M = 54 degrees, and we know the measures of arcs AT and TH in the circle, we can find m∠T and m∠H.
m∠T = 50 degrees (from the arc joining A and T)
m∠H = 170 degrees (from the arc joining T and H)
Now we can substitute these values into the equation:
m∠A + 54 + 50 + 170 = 360
m∠A + 274 = 360
m∠A = 360 - 274
m∠A = 86 degrees
Therefore, the measure of angle A is 86 degrees.
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