Find the large angle of a parallelogram if its two angles are 1:71 apart.

A parallelogram is a quadrangle in which opposite sides are parallel and equal to each other. The opposite angles of the parallelogram are also equal:

∠А = ∠С;

∠В = ∠D.

Since the sum of all four angles of a parallelogram is 360º, and its angles are related as 1:71, then we express:

x is the degree measure of the angles ∠А and ∠С;

71x – the degree measure of the angles ∠В and ∠D;

x + x + 71x + 71x = 360;

144x = 360;

x = 360/144 = 2.5º

∠В = ∠D = 2.5 · 71 = 177.5º.

Answer: The degree measure of the larger parallelogram angle is 177.5 degrees.