A rhombus is a parallelogram with four equal sides.

Question

Each of the two larger angles of a rhombus is 17 times as large as the two smaller angles. Find the measure of each of the four angles.

Answer 1

For a rhombus, the sum of the two larger (equal) angles and the two smaller (equal) angles sum up to 360°.

 

 

Let y = the larger angle and x = the smaller angle.

 

 

y = 17x   for the relationship between larger and smaller angles

 

2y + 2x = 360   for the total interior angle of the rhombus.

 

 

2(17x) + 2x = 360

 

34x + 2x = 36x = 360

 

x = 10° and y = 170°