Two base angles of a cyclic quadrilateral are 90 and 60 find other remaining two angles.
In any cyclic quad, the opposite angles are supplementary, that is, they add up to 180°
The two base angle of a cyclic quadrilateral are 90 60 find the other reaming
To find the other two angles of a cyclic quadrilateral given two base angles, we need to use the property that the opposite angles in a cyclic quadrilateral are supplementary (i.e., their sum is 180 degrees).
Given that two base angles are 90 and 60 degrees, let's denote the remaining two angles as x and y.
Since the opposite angles are supplementary, we can write two equations based on this property:
Equation 1: x + 90 = 180 (opposite angles in a cyclic quadrilateral are supplementary)
Equation 2: y + 60 = 180 (opposite angles in a cyclic quadrilateral are supplementary)
Solving Equation 1:
x + 90 = 180
Subtracting 90 from both sides:
x = 180 - 90
x = 90 degrees
Solving Equation 2:
y + 60 = 180
Subtracting 60 from both sides:
y = 180 - 60
y = 120 degrees
Therefore, the other two remaining angles of the cyclic quadrilateral are 90 degrees and 120 degrees.