Two adjacent angles from resulting angle with measures 160. m <1 = 3x and m <2 = ( 2x + 10 ). Solve for x What are the two unknown angles' measurements?

Question

m<1 = _, m <2 = _

Answer 1

To find the value of $x$ and the measures of the two angles, we start with the given equations for the angles:

• $m\mathrm{\angle }1=3x$
• $m\mathrm{\angle }2=2x+10$

We know that the sum of the measures of the two angles is 160 degrees, so we can set up the equation:

$$m\mathrm{\angle }1+m\mathrm{\angle }2=160$$

Substituting the expressions for the angles into the equation gives us:

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

Now, combine like terms:

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

Next, subtract 10 from both sides:

$$5x=150$$

Now, divide by 5:

$$x=30$$

Now that we have $x$, we can find the measures of the two angles.

For $m\mathrm{\angle }1$:

$$m\mathrm{\angle }1=3x=3(30)=90$$

For $m\mathrm{\angle }2$:

$$m\mathrm{\angle }2=2x+10=2(30)+10=60+10=70$$

Thus, the measures of the two angles are:

$$m\mathrm{\angle }1={90}^{\circ },m\mathrm{\angle }2={70}^{\circ }$$

Final answer:

• $m\mathrm{\angle }1={90}^{\circ }$
• $m\mathrm{\angle }2={70}^{\circ }$