Question

Can someone help me solve this? I will need the x and y and will also need to solve for angles 1, 2, 3, and 4.

Answer 1

Answer:

x = 20,

y = 15

m<1 = 75°

m<2 = 75°

m<3 = 75°

m<4 = 105°

Step-by-step explanation:

m<1 = 3x + 15

m<2 = 4x - 5

m<3 = 5y

✔️m<1 = m<2 (corresponding angles are congruent)

3x + 15 = 4x - 5 (substitution)

Collect like terms

3x - 4x = -15 - 5

-x = -20

Divide both sides by -1

x = 20

✔️m<3 = m<2 (corresponding angles are congruent)

5y = 4x - 5 (substitution)

Plug in the value of x and solve for y

5y = 4(20) - 5

5y = 80 - 5

5y = 75

5y/5 = 75/5

y = 15

✔️Find the measure of each labelled angle:

x = 20, y = 15

Thus:

m<1 = 3x + 15 = 3(20) + 15

m<1 = 75°

m<2 = 4x - 5 = 4(20) - 5

m<2 = 75°

m<3 = 5y = 5(15)

m<3 = 75°

m<4 + m<3 = 180° (same side interior angles are supplementary)

m<4 + 75° = 180° (substitution)

m<4 = 180° - 75° (subtraction property of equality)

m<4 = 105°