Question

select all the true statements. (2x + 1)° (x + 15)° x° 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: Use angle - sum property of a triangle

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

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

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

Step4: Compare the angles

Since \(m\angle B = 41^{\circ}\), \(m\angle C=56^{\circ}\), and \(m\angle A = 83^{\circ}\), the order from smallest to largest is \(\angle B,\angle C,\angle A\).

Answer:

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