Answer:
m∠A = 15°; m∠B = 89°; m∠C = 76°
Step-by-step explanation:
The sum of the three interior angles of a triangle is 180°.
Let x = m∠A
Then 3x + 44 = m∠B
and x + 61 = m∠C
x + 3x + 44 + x + 61 = 180
5x + 105 = 180
5x = 75
x = 15
m∠A = 15°
m∠B = 3(15) + 44 = 45 + 44 = 89°
m∠C = 15 + 61 = <u> 76°</u>
Sum = 180°
We know that the figure has a symmetry
angle 1 = angle 2
angle 1 =180°-(18°+90°) = 180° - 108°=72°
Therefore, <em><u>angle 2 =72°</u></em><em><u>.</u></em>
278°
m arc BAC = 360 -(2×41)
= 360 - 82 = 278°