Question

which of the following statements are true? select all that apply
a. $(4x + 16)^{circ}=180^{circ}$
b. $x^{circ}=49^{circ}$
c. $mangle a = 99^{circ}$
d. from smallest to largest: $angle b, angle c, angle a$

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 15)+(2x + 1)+x=180\).
Combine like terms: \(4x+16 = 180\). So, option A is correct.

Step2: Solve the equation for \(x\)

Subtract 16 from both sides of \(4x + 16=180\): \(4x=180 - 16=164\).
Divide both sides by 4: \(x=\frac{164}{4}=41\). So, option B (\(x = 49\)) is incorrect.

Step3: Calculate the measures of the angles

\(\angle B=x = 41^{\circ}\), \(\angle C=x + 15=41+15 = 56^{\circ}\), \(\angle A=2x + 1=2\times41+1=83^{\circ}\).
So, \(m\angle A=83^{\circ}\), option C (\(m\angle A = 99^{\circ}\)) is incorrect.

Step4: Order the angles

Since \(41^{\circ}<56^{\circ}<83^{\circ}\), the order from smallest to largest is \(\angle B,\angle C,\angle A\). So, option D is correct.

Answer:

A. \((4x + 16)^{\circ}=180^{\circ}\), D. From smallest to largest: \(\angle B,\angle C,\angle A\)