Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
49°
(8x+19)°
77°
answer attempt 1 out of 2
x =
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Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(49 + 77 + (8x + 19) = 180\).

Step2: Simplify the left side

Calculate \(49 + 77 + 19 = 145\), so the equation becomes \(145 + 8x = 180\).

Step3: Solve for x

Subtract 145 from both sides: \(8x = 180 - 145 = 35\)? Wait, no, 180 - 145 is 35? Wait, 49 +77 is 126, 126 +19 is 145. 180 -145 is 35? Wait, no, 8x = 180 - 49 -77 -19. Let's recalculate: 49 +77 = 126, 126 +19 = 145. 180 -145 = 35? Wait, no, 8x = 180 - (49 +77 +19) = 180 - 145 = 35? Then x = 35/8? Wait, that can't be. Wait, maybe I miscalculated. Wait, 49 +77 is 126, 126 +19 is 145. 180 -145 is 35. Then 8x = 35? No, wait, the angle is (8x +19). Wait, maybe I made a mistake. Wait, let's do it again. The three angles: 49°, 77°, and (8x +19)°. Sum to 180°. So 49 + 77 + 8x + 19 = 180. Combine like terms: 49 +77 is 126, 126 +19 is 145. So 145 + 8x = 180. Subtract 145: 8x = 35? Wait, 180 -145 is 35? Then x = 35/8 = 4.375? But that seems odd. Wait, maybe the angle is (8x + 19)? Wait, maybe I misread the angle. Wait, the figure shows (8x +19)°, 49°, and 77°. Wait, maybe the angle is (8x + 19), but maybe I added wrong. Wait, 49 +77 is 126, 180 -126 is 54. So 8x +19 = 54. Then 8x = 54 -19 = 35? No, 54 -19 is 35? Wait, 54 -19 is 35? Then 8x = 35, x = 35/8 = 4.375. Wait, that's correct? Wait, 84.375 = 35, 35 +19 = 54. 49 +77 +54 = 180. 49+77=126, 126+54=180. Yes, that works. So x = 35/8? Wait, no, 8x +19 = 54. So 8x = 54 -19 = 35? Wait, 54 -19 is 35? Yes. So x = 35/8 = 4.375? But maybe the problem has a typo, or I misread the angle. Wait, maybe the angle is (8x + 1)°? No, the user wrote (8x +19)°. So according to the calculation, x = 35/8 = 4.375. But let's check again. 49 +77 + (84.375 +19) = 49 +77 + (35 +19) = 49 +77 +54 = 180. Yes, that's correct. So x = 35/8 = 4.375, which is 4.375 or 35/8. But maybe the problem expects an integer. Wait, maybe I misread the angle. Wait, maybe the angle is (8x + 1)°? No, the user's figure shows (8x +19)°. So the calculation is correct.

Wait, maybe I made a mistake in addition. 49 +77: 49 +70=119, 119+7=126. 126 +19: 126+20=146, minus 1=145. 180-145=35. 8x=35. x=35/8=4.375. So that's the answer.

Answer:

\( x = \frac{35}{8} \) (or 4.375)