Question

3×3 systems applications
the interior angles of a triangle sum to 180°. the measure of ∠a is four degrees more than the sum of ∠b and ∠c. if ∠a measures 4° more than ∠c, what is the measure of each angle?
1 declare your variables
a =
b =
c =
2 write the system of equations
eq.1
eq.2
eq.3
3 solve the system
m∠a =
m∠b =
m∠c =
4 explain your process
which method did you use to solve the problem? explain your process.

Explanation:

Step1: Declare variables

Let $a$ be the measure of $\angle A$, $b$ be the measure of $\angle B$, and $c$ be the measure of $\angle C$.

Step2: Write equations

• EQ.1: Since the sum of interior - angles of a triangle is $180^{\circ}$, we have $a + b + c=180$.
• EQ.2: The measure of $\angle A$ is four degrees more than the sum of $\angle B$ and $\angle C$, so $a=b + c+4$.
• EQ.3: $\angle A$ measures $47^{\circ}$ more than $\angle C$, so $a=c + 47$.

Step3: Substitute and solve

• Substitute $a=b + c+4$ into $a + b + c=180$. We get $(b + c+4)+b + c=180$, which simplifies to $2b + 2c=176$, then $b + c = 88$, and $b=88 - c$.
• Substitute $a=c + 47$ into $a=b + c+4$. We get $c + 47=b + c+4$, then $b = 43$.
• Since $b = 43$ and $b + c=88$, then $43 + c=88$, so $c=45$.
• Since $a=c + 47$, then $a=45 + 47=92$.

Answer:

$m\angle A = 92^{\circ}$, $m\angle B = 43^{\circ}$, $m\angle C = 45^{\circ}$