Question

97 POINTS WILL MARK BRAINLESS

Answer 1

(1)

(a)

the sum of the angles in a triangle = 180°, hence

3x + 15 + 15x - 10 + 15x + 10 = 180

33x + 15 = 180 ( subtract 15 from both sides )

33x = 165 ( divide both sides by 33 )

x = 5

(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°

(2)

2x + 15 + 135 = 180 ( straight angle )

2x + 150 = 180 ( subtract 150 from both sides )

2x = 30 ( divide both sides by 2 )

x = 15 ⇒ 2x + 15 = 45

∠1 = 45° ( alternate angles are congruent )

Answer 2

Answer:

2.

• x = 15
• ∠1 = 45°

1.

• x = 5
• ∠A = 85°

Step-by-step explanation:

2.

Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). 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 m and n. This makes them alternate interior angles. 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°.

1.

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°