Question

solve for the value of m.
84°
(5m+1)°
answer attempt 1 out of 3
m =
submit answer

Explanation:

Step1: Identify angle relationship

The three angles (84°, (5m + 1)°, and the straight angle) sum to 180°? Wait, no—wait, the two angles 84° and (5m + 1)° and the vertical? Wait, no, looking at the diagram, the two angles 84° and (5m + 1)° are adjacent and form a straight line? Wait, no, the diagram shows two rays with a common vertex, and the angles between them: 84° and (5m + 1)°, and the other angle? Wait, no, actually, the three angles? Wait, no, the straight line (180°) is formed by the two angles 84° and (5m + 1)°? Wait, no, wait, the diagram has three rays? Wait, no, the diagram: one vertical ray (up and down), and a horizontal? No, the diagram: the two angles 84° and (5m + 1)° are adjacent, and together with the straight angle? Wait, no, actually, the sum of 84° and (5m + 1)° should be 180°? Wait, no, wait, the straight line is 180°, so 84 + (5m + 1) = 180? Wait, no, wait, maybe the two angles are supplementary? Wait, let's check: if the two angles are adjacent and form a straight line, their sum is 180°. So 84 + (5m + 1) = 180.

Step2: Solve the equation

So, 84 + 5m + 1 = 180
Combine like terms: 85 + 5m = 180
Subtract 85 from both sides: 5m = 180 - 85 = 95
Divide both sides by 5: m = 95 / 5 = 19

Wait, but wait, maybe the angles are complementary? No, 84 + (5m + 1) = 90? But 84 is already more than 90, so no. So it must be supplementary (sum to 180°). So the equation is 84 + (5m + 1) = 180.

Wait, let's recheck: 84 + (5m + 1) = 180
85 + 5m = 180
5m = 180 - 85 = 95
m = 95 / 5 = 19. Yes, that makes sense.

Answer:

\( m = 19 \)