+1450 The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is 129 degrees, what is the measure of the second largest angle, in degrees?
Thanks :D
Sum = [First term + last term] / 2 x Number of terms
360 =[F + 129] / 2 x 4, solve for F
720 =[F + 129] x 4
180 =[F + 129]
F = 180 - 129
F =51 degrees - the smallest angle
N =[L - F] / D + 1
4 =[129 - 51] / D
3 =[78] /D
3D = 78
D = 78/3
D =26 - diffrence between the 4 angles
51+26 =77 degrees - the second smallest angle
77+26 =103 degrees - the second largest angle. So that you have:
51, 77, 103, 129 angles in degrees.
+128474 The interior angles of a quadrilateral sum to 360°
Let a1 be the smallest angle and d be the common difference between the angles
So we have the following equation
129 = a1 + 3d ⇒ 129 - 3d = a1 (1)
And
a1 + (a1 + d) + (a1 + 2d ) + 129 = 360 (2)
Sub (1) into (2) and simplifying we have that
129 - 3d + (129 - 2d) + ( 129 - d) + 129 = 360
516 - 6d = 360 rearrrange as
516 - 360 = 6d
156 = 6d divide both sides by 6
26 = d
And using (1) we have that 129 - 3(26) = a1 = 51°
So.....the second largest angle is 51 + 2(26) = 103°
