Answer:
2.
1.
Step-by-step explanation:
<h3>2.</h3>
Angles 135° and (2x+15)° together make up a line (the transversal crossing <em>m</em> and <em>n</em>). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...
... 135° + (2x+15)° = 180°
... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms
... 2x = 30 . . . . . . . . . . . . subtract 150
... x = 15 . . . . . . . . . . . . . . divide by 2
Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines <em>m</em> and <em>n</em>. This makes them <em>alternate interior angles</em>. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.
<h3>1.</h3>
a) The sum of angles in a triangle is always 180°. This means ...
... (15x +10)° + (15x -10)° + (3x +15)° = 180°
... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms
... 33x = 165 . . . . . . . . . . subtract 15
... x = 5 . . . . . . . . . . . . . . . divide by 33
b) ∠A = (15x+10)° = (15·5 +10)°
... ∠A = 85°