There are angles whose measures add to 180°

Question

. Their measures are: m∠A=67°
, m∠B=(2x+20)°
, and m∠C=x°
. What is the measure of ∠B
?(1 point)
Responses

62°
62 degrees

31°
31 degrees

180°
180 degrees

82°

Answer 1

To find the measure of angle $\mathrm{\angle }B$, we start by using the fact that the measures of angles $m\mathrm{\angle }A$, $m\mathrm{\angle }B$, and $m\mathrm{\angle }C$ add up to 180°.

Given:

• $m\mathrm{\angle }A=67°$
• $m\mathrm{\angle }B=(2x+20)°$
• $m\mathrm{\angle }C=x°$

We can set up the equation:

$$m\mathrm{\angle }A+m\mathrm{\angle }B+m\mathrm{\angle }C=180°$$

Substituting the given values:

$$67°+(2x+20)°+x°=180°$$

Combining like terms gives:

$$67+2x+20+x=180$$

Which simplifies to:

$$87+3x=180$$

Next, we isolate $3x$:

$$3x=180-87$$ $$3x=93$$

Now, we solve for $x$:

$$x=\frac{93}{3}=31$$

Now that we have $x$, we can find $m\mathrm{\angle }B$:

$$m\mathrm{\angle }B=2x+20=2(31)+20=62+20=82°$$

Therefore, the measure of $\mathrm{\angle }B$ is $\boxed{{\displaystyle 82°}}$.