Question

question 3 1 pts if the ratio of two supplementary angles is 4 to 19, calculate the measu of the larger of the two angles. 157.68 131.36 148.7 136.06 none of these answers are correct.

Explanation:

Step1: Recall supplementary angles sum to 180°

Let the two angles be \(4x\) and \(19x\). Since they are supplementary, \(4x + 19x=180^\circ\).

Step2: Solve for \(x\)

Combine like terms: \(23x = 180^\circ\). Then \(x=\frac{180}{23}\approx7.826\).

Step3: Find the larger angle (\(19x\))

Multiply \(x\) by 19: \(19\times\frac{180}{23}=\frac{3420}{23}\approx148.7\). Wait, but let's check again. Wait, \(4 + 19 = 23\), so the larger angle is \(\frac{19}{23}\times180\). Let's calculate \(\frac{19\times180}{23}=\frac{3420}{23}\approx148.69565\approx148.7\). But wait, the options have 148.7 as an option? Wait, no, wait the original problem's options: let's re - calculate. Wait, \(180\div23\approx7.826\), \(19\times7.826 = 148.694\approx148.7\). But wait, maybe I made a mistake. Wait, no, supplementary angles sum to 180. Ratio 4:19, so total parts 23. Each part is \(180/23\approx7.826\). Larger angle is \(19\times7.826\approx148.7\). But wait, the option 148.7 is there. Wait, but let's check the calculation again. \(180\times19 = 3420\), \(3420\div23 = 148.69565\approx148.7\). So the answer should be 148.7. But wait, the options: one of them is 148.7. Wait, but let's check the problem again. Wait, maybe I misread the ratio. Wait, the ratio is 4 to 19. So 4x and 19x, sum to 180. So 23x = 180, x = 180/23≈7.826, 19x≈148.7. So the answer is 148.7.

Answer:

148.7