Question

select all the true statements. 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, we get $2x+1+x + 15+x=180$, which simplifies to $4x+16 = 180$.

Step2: Solve for x

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

Step3: Find the measure of each angle

For $\angle A$: $m\angle A=2x + 1=2\times41+1=82 + 1=83$.
For $\angle B$: $m\angle B=x = 41$.
For $\angle C$: $m\angle C=x + 15=41+15=56$.
Since $41<56<83$, the order of the angles 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. $m\angle C = 56$