Question

congruent triangles quiz
which of the following statements are true? select two that apply.
(2x + 1)°
(x + 15)°
x°
□x° = 40°
□m∠a = 99°
□from smallest to largest, ∠b, ∠c, ∠a
□(4x + 16)° = 150°

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $(2x + 1)+(x + 15)+x=180$.
Combining like - terms, we get $4x+16 = 180$.

Step2: Solve for x

Subtract 16 from both sides of the equation $4x+16 = 180$:
$4x=180 - 16=164$.
Then divide both sides by 4: $x=\frac{164}{4}=41$.

Step3: Find the measure of each angle

$\angle A=(2x + 1)^{\circ}=(2\times41 + 1)^{\circ}=83^{\circ}$.
$\angle C=(x + 15)^{\circ}=(41+15)^{\circ}=56^{\circ}$.
$\angle B=x^{\circ}=41^{\circ}$.

Step4: Analyze the statements

• For $x = 41^{\circ}$, the statement $x = 40^{\circ}$ is false.
• $\angle A=83^{\circ}

eq99^{\circ}$, so the statement $m\angle A = 99^{\circ}$ is false.

• Since $\angle B = 41^{\circ},\angle C = 56^{\circ},\angle A = 83^{\circ}$, the order from smallest to largest is $\angle B,\angle C,\angle A$, so this statement is true.
• Since $x = 41$, then $4x+16=4\times41 + 16=164 + 16=180

eq150$, so the statement $(4x + 16)^{\circ}=150^{\circ}$ is false.

Answer:

From smallest to largest, $\angle B,\angle C,\angle A$