Question

use structure select the angles and sides of the triangle that are listed in order from smallest to largest.
x
(2x + 9)°
y
(2x + 1)°
z
a) ∠z, ∠x, ∠y, xz, xy, yz
b) ∠x, ∠y, ∠z, yz, xz, xy
c) ∠y, ∠z, ∠x, yz, xz, xy
d) ∠x ∠y ∠z yz xy yz

Explanation:

Step1: Sum of angles in triangle

Sum = 180°: $(2x+1)+(2x+9)+90=180$
Simplify: $4x+100=180 → 4x=80 → x=20$

Step2: Calculate angle measures

∠X: $2(20)+1=41°$
∠Y: $2(20)+9=49°$
∠Z: 90°

Order of angles (smallest→largest): ∠X, ∠Y, ∠Z

Step3: Match sides to opposite angles

Side opposite ∠X: $\overline{YZ}$
Side opposite ∠Y: $\overline{XZ}$
Side opposite ∠Z: $\overline{XY}$

Order of sides (smallest→largest): $\overline{YZ}$, $\overline{XZ}$, $\overline{XY}$

Answer:

B) ∠X, ∠Y, ∠Z, $\overline{YZ}$, $\overline{XZ}$, $\overline{XY}$