Question

There are angles whose measures add to 180° . Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ? Please

Answer 1

To find the measure of angle \( B \), we first set up the equation based on the fact that the measures of angles \( A \), \( B \), and \( C \) add up to \( 180^\circ \):

\[
m\angle A + m\angle B + m\angle C = 180^\circ
\]

Substituting the given expressions:

\[
67^\circ + (2x + 20)^\circ + x^\circ = 180^\circ
\]

Now, we combine the like terms:

\[
67 + 2x + 20 + x = 180
\]

Simplifying the left side:

\[
87 + 3x = 180
\]

Next, we isolate \( x \) by subtracting \( 87 \) from both sides:

\[
3x = 180 - 87
\]

This simplifies to:

\[
3x = 93
\]

Now, we divide both sides by \( 3 \):

\[
x = 31
\]

Now that we have the value of \( x \), we can find the measure of angle \( B \):

\[
m\angle B = 2x + 20
\]

Substituting the value of \( x \):

\[
m\angle B = 2(31) + 20
\]

Calculating this gives:

\[
m\angle B = 62 + 20 = 82^\circ
\]

Thus, the measure of angle \( B \) is:

\[
\boxed{82^\circ}
\]