NAEP Grade 8 Geometry. Practice it free.

The two congruent angles total $2 \times 61.7^{\circ} = 123.4^{\circ}$, so $\angle K = 180^{\circ} - 123.4^{\circ} = 56.6^{\circ}$.

$(6-2) \times 180 = 4 \times 180 = 720$.

The sum of the interior angles of a triangle is $180^{\circ}\textsf{.}$ So $m\angle C = 180^{\circ} - 50^{\circ} - 78^{\circ} = 52^{\circ}\textsf{.}$

$\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$.

Let the missing leg be $x$. Then $x^{2} + 24^{2} = 26^{2}$, so $x^{2} = 26^{2} - 24^{2} = 676 - 576 = 100$ and $x = \sqrt{100} = 10$.

$3^{2} + 4^{2} = 9 + 16 = 25$, so the hypotenuse is $\sqrt{25} = 5\textsf{.}$

The ramp is the hypotenuse of a right triangle with legs $5$ and $12$: $\sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$ feet.

Area $A = \ell w$, so $120 = 8w$ and $w = 15$. The diagonal is the hypotenuse of a right triangle with legs $8$ and $15$: $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$