Questions: Find each length and angle measure for rectangle GHJK. Round to the nearest tenth. m angle GHK HL

Solution Steps

Since GHJK is a rectangle, all of its interior angles are right angles. Therefore, $m \angle GHK = 90^{\circ}$.

The diagonals of a rectangle are congruent and bisect each other. Thus, the length of diagonal $HJ$ is equal to the length of diagonal $GK$. We are given $HJ = 7 + 7 = 14$. Since the diagonals bisect each other, $HL = \frac{1}{2} HJ$. Therefore, $HL = \frac{1}{2}(14) = 7$.

Since GHJK is a rectangle, $GH = JK = 10$ and $HJ = GK = 14$. Also, all angles are right angles, so $\angle G = 90^{\circ}$. We can use the Pythagorean theorem on right triangle $GHJ$ to find $GJ$. \(GJ^2 = GH^2 + HJ^2\) \(GJ^2 = 10^2 + 7^2\) \(GJ^2 = 100 + 49\) \(GJ^2 = 149\) \(GJ = \sqrt{149}\) \(GJ \approx 12.2\)

Final Answer