Question

hint: m∠1 = x; m∠3 = 2x +6; m∠2 = 2x + 6 - 27. the measure of a straight line is 180 degrees.
10 read and solve
the problem below:
∠1, ∠2, and ∠3 form
a straight line. if m∠3
is six more than twice
m∠1 and m∠2 is 27 less
than m∠3, find m∠2.
a) 57° film a music video
b) 39° make their parents proud
c) 105° get out of math class
d) 61° win a cruise to the bahamas
e) 84° inspire people

Explanation:

Step1: Define angle measures

Let $m\angle1 = x$. Then $m\angle3 = 2x + 6$, and $m\angle2 = (2x + 6) - 27 = 2x - 21$.

Step2: Sum angles to 180°

Since the angles form a straight line:
$$x + (2x - 21) + (2x + 6) = 180$$

Step3: Simplify the equation

Combine like terms:
$$5x - 15 = 180$$

Step4: Solve for x

Isolate $x$:
$$5x = 180 + 15 = 195$$
$$x = \frac{195}{5} = 39$$

Step5: Calculate $m\angle2$

Substitute $x=39$ into $m\angle2 = 2x - 21$:
$$m\angle2 = 2(39) - 21 = 78 - 21 = 57$$

Answer:

A) $57^\circ$ film a music video