Question

Geometry - 50 points :D

Answer 1

See below!

Explanation:

From the figure,

∠8 = ∠4 (Corresponding angles are equal)

So,

∠8 = 2x + 27

Also,

∠5 = ∠7 (Vertically opposite angles are equal)

∠5 = 3x - 22

Statement:

• Angles on a straight line add up to 180 degrees.

Solution:

So,

∠8 + ∠5 = 180°

2x + 27 + 3x - 22 = 180

• Combine like terms

2x + 3x + 27 - 22 = 180

5x + 5 = 180

• Subtract 5 from both sides

5x = 180 - 5

5x = 175

• Divide both sides by 5

x = 175 / 5

x = 35

So,

∠8 = 2x + 27

∠8 = 2(35) + 27

∠8 = 70 + 27

∠8 = 97°

Now,

∠5 = 3x - 22

∠5 = 3(35) - 22

∠5 = 105 - 22

∠5 = 83°

`\rule[225]{225}{2}`