Given circle B, and points A, C and D on the circle. AC is not a diameter, and D is on the major arc ADC. and angle ADC = 80 degrees. what is the measure of angle BAC?
Easy.
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2006-07-05 00:56:05 · 5 answers · asked by kevin! 5 in Science & Mathematics ➔ Mathematics
Is B the centre of the circle?
If so, then BAC is 10 degrees.
Why? Well, The angle subtended by a point on the major arc of a chord is equal to one half the angle subtended by the centre of the circle. So that gives the angle ABC as 160 degrees. Then, since BAC is an isoceles triangle, BAC = BCA = 10 degrees.
2006-07-05 01:26:35 · answer #1 · answered by fatal_flaw_death 3 · 0⤊ 0⤋
In this circle angleABC is double the angle ADC.
angle ADC=80.
angle ABC=2*80=160
In triangle ABC, AB=BC as both are the radii.
AB=BC implies angle BAC= angle BCA (let x)
In a triangle sum of the angles is 180 deg.
So, 160+x+x=180
160+2x=180
2x=180-160
2x=20
x=10
Hence angle BAC=10 deg.
2006-07-06 09:04:32 · answer #2 · answered by K N Swamy 3 · 0⤊ 0⤋
angle ABC= twice of angle ADC
= 160degrees
angle ABC+angle BAC+angle ACB=180 degrees
and, angle BAC= angle ACB
therefore, angle BAC=10 degrees.
2006-07-05 08:27:26 · answer #3 · answered by kahefneg 1 · 0⤊ 0⤋
angle ABC is 2xangleADC, and angle BAC=ACB (ABC is an isoceles triangle), so angle BAC = 1/2{180 - (80x2)} = 1/2 (20) = 10 degree...
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2006-07-05 12:56:49 · answer #4 · answered by momiji 1 · 0⤊ 0⤋
Is it 280 degrees?
2006-07-05 08:05:38 · answer #5 · answered by Squirrel 3 · 0⤊ 0⤋