Question

Consider rhombus GHIJ with diagonals IG and HJ. If m∠GJP=34 ∘, find m∠GJI, 146 ∘56 ∘68 ∘34 ∘112 ∘ None of the above

Answer 1

The measure of angle GJI in rhombus GHIJ is 68 degrees, calculated by understanding that the diagonals of a rhombus are perpendicular bisectors, making angle GJI twice the measure of angle GJP, which is 34 degrees.

Step-by-step explanation:

To find the measure of angle GJI in rhombus GHIJ, we first need to understand that the diagonals in a rhombus are perpendicular bisectors of each other. Therefore, they divide each angle into two congruent angles. Given that m∠GJP is 34 degrees, and GJP is half of the angle formed by diagonal HJ and side JP, the total angle at GJ would be twice that, because diagonal HJ cuts ∠GJI in half to create two 34-degree angles.

m∠GJI = 2 * m∠GJP
= 2 * 34 degree
= 68 degrees.

Therefore, the measure of angle GJI in rhombus GHIJ is 68 degrees.