Two adjacent angles form a resulting angle with measure 160° . m∠1=3x° and m∠2=(2x+10)° . Solve for x . What are the two unknown angles’ measurements?(1 point)

Question

m∠1= ___°, m∠2=____ 

Answer 1

To find the value of $x$ and the measures of the two angles, we start with the information given in the problem.

The two angles are:

• $m\angle 1=3x°$
• $m\angle 2=(2x+10)°$

According to the problem, these two angles are adjacent and form a resulting angle of $160°$. Therefore, we can set up the equation:

$$m\angle 1+m\angle 2=160°$$

Substituting the expressions for $m\angle 1$ and $m\angle 2$:

$$3x+(2x+10)=160$$

Now, simplify this equation:

$$3x+2x+10=160$$ $$5x+10=160$$

Next, isolate $x$ by first subtracting $10$ from both sides:

$$5x=160-10$$ $$5x=150$$

Now, divide by $5$:

$$x=\frac{150}{5}$$ $$x=30$$

Now that we have $x=30$, we can find the measures of the angles:

For $m\angle 1$:

$$m\angle 1=3x=3(30)=90°$$

For $m\angle 2$:

$$m\angle 2=2x+10=2(30)+10=60+10=70°$$

Now we confirm if the sum is $160°$:

$$m\angle 1+m\angle 2=90°+70°=160°$$

This verification is correct. Thus, the measures of the angles are:

• $m\angle 1=90°$
• $m\angle 2=70°$

So the final answer is:

• $m\angle 1=90°$
• $m\angle 2=70°$