In order to find all the angles of a parallelogram, we will compose and solve an equation.
But first of all, let’s remember the properties of the parallelogram angles.
Opposite angles are equal to each other, and the sum of the angles adjacent to one side is 180 °.
It is known from the condition that one of the angles of the parallelogram is 46 ° larger than the other.
Let’s denote by x ° the smaller angle of the parallelogram, then (x + 46) °.
Let’s make the equation:
x + (x + 46) = 180;
x + x + 46 = 180;
2x + 46 = 180;
2x = 180 – 46;
2x = 134;
x = 134: 2;
x = 67 ° smaller angle, then 67 + 46 = 113 °.
Answer: 67 °; 67 °; 113 °; 113 °.
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