Question

the diagram shows a triangle.

what is the value of u?

write your answer as an integer or as a decimal rounded to the nearest tenth.

u =

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Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((u + 13^\circ)+(u + 20^\circ)+(5u + 11^\circ)=180^\circ\).

Step2: Combine like terms

Simplify the left - hand side: \(u+13 + u + 20+5u + 11=180\). Combining like terms gives \(7u+44 = 180\).

Step3: Solve for u

Subtract 44 from both sides: \(7u=180 - 44=136\). Then divide both sides by 7: \(u=\frac{136}{7}\approx19.4\) (rounded to the nearest tenth). Wait, wait, let's recalculate: \(180-(13 + 20+11)=180 - 44 = 136\), \(136\div7 = 19.428\cdots\approx19.4\)? Wait, no, wait: \(u + 13+u + 20+5u+11=(u + u+5u)+(13 + 20+11)=7u + 44\). So \(7u=180 - 44=136\), \(u=\frac{136}{7}\approx19.4\)? Wait, no, 719 = 133, 136 - 133 = 3, so \(u = 19+\frac{3}{7}\approx19.4\)? Wait, no, 136 divided by 7: 719 = 133, 136 - 133 = 3, so 19.428..., rounded to the nearest tenth is 19.4? Wait, no, maybe I made a mistake. Wait, 13 + 20+11 is 44, 180 - 44 is 136. 136 divided by 7: 7*19 = 133, 136 - 133 = 3, so 19.428, so to the nearest tenth is 19.4? Wait, but let's check again. Wait, the sum of angles in a triangle is 180. So:

\((u + 13)+(u + 20)+(5u + 11)=180\)

\(u+13+u + 20+5u+11 = 180\)

\(7u+44 = 180\)

\(7u=180 - 44=136\)

\(u=\frac{136}{7}\approx19.4\) (rounded to the nearest tenth). Wait, but maybe I miscalculated the sum of the constants. 13+20 is 33, 33 + 11 is 44. Yes. So 7u=136, u = 136/7≈19.4.

Wait, no, wait 136 divided by 7: 7*19 = 133, 136-133 = 3, so 19.428, so to the nearest tenth is 19.4.

Answer:

\(19.4\)