Question

select all the true statements.
a
(2x + 1)°
(x + 15)°
c
x°
b
□ a. (4x + 16) = 180
□ b. x = 49
□ c. m∠a = 99
□ d. from smallest to largest: ∠b, ∠c, ∠a
□ e. m∠c = 56

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((2x + 1)+(x + 15)+x=180\). Combine like - terms: \(2x+1+x + 15+x=180\), which simplifies to \(4x+16 = 180\).

Step2: Solve the equation 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

\(m\angle A=2x + 1=2\times41+1=82 + 1=83^{\circ}\).
\(m\angle B=x = 41^{\circ}\).
\(m\angle C=x + 15=41+15=56^{\circ}\).

Step4: Check each statement

• For statement A: We derived \(4x + 16=180\), so statement A is true.
• For statement B: We found \(x = 41

eq49\), so statement B is false.

• For statement C: \(m\angle A=83

eq99\), so statement C is false.

• For statement D: Since \(m\angle B = 41^{\circ}\), \(m\angle C = 56^{\circ}\), and \(m\angle A=83^{\circ}\), from smallest to largest, the angles are \(\angle B,\angle C,\angle A\). So statement D is true.
• For statement E: \(m\angle C=56^{\circ}\), so statement E is true.

Answer:

A. \((4x + 16)=180\)
D. From smallest to largest: \(\angle B,\angle C,\angle A\)
E. \(m\angle C = 56\)