Question

NEED ANSWER ASAP
any answers are appreciated

part a. use the diagram to write an equation and solve for x. show your work

part b. use your answer from part a for x, and find the measure of both angles. select two answers
- 116
- 68
- 61
- 112
- 119
- 64​

Answer 1

Answer:

×= 38

2x-15 = 61°

3×+5= 119°

Step-by-step explanation:

2×-15+3x +5= 180

180+10= 190

190 ÷5x

×=38

Answer 2

Answer:

a)  x = 38

b)  61° and 119°

Step-by-step explanation:

Same-side Exterior Angles Theorem

When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).

Part (a)

Using the Same-side Exterior Angles Theorem, equate the sum of the two angles to 180° and solve for x:

⇒ (2x - 15)° + (3x + 5)° = 180°

⇒ 2x - 15 + 3x + 5 = 180

⇒ 5x - 10 = 180

⇒ 5x = 190

⇒ x = 38

Part (b)

Substitute the found value of x from part (a) into the expressions for each angle:

⇒ (2x - 15)°

⇒ (2(38) - 15)°

⇒ (76 - 15)°

⇒ 61°

⇒ (3x + 5)°

⇒ (3(38) + 5)°

⇒ (114 + 5)°

⇒ 119°

Therefore, the two angles are 61° and 119°.