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 =
submit
next up
done for now? try these next:
interior angles of polygons
find missing angles in triangles using ratios
angle - angle criterion for similar triangles
proofs involving triangles i
missing angles in diagrams: mixed review
congruency in isosceles and equilateral triangles
angle - side relationships in triangles
area of a triangle: law of sines

Explanation:

Step1: Use the triangle angle sum theorem

The sum of interior angles in a triangle is \(180^{\circ}\). So, \((u + 29)+(25u-27)+(21u + 45)=180\).

Step2: Combine like - terms

Combine the \(u\) terms: \(u+25u + 21u=47u\). Combine the constant terms: \(29-27 + 45=47\). The equation becomes \(47u+47 = 180\).

Step3: Solve for \(u\)

Subtract \(47\) from both sides: \(47u=180 - 47\), so \(47u=133\). Then \(u=\frac{133}{47}\approx2.8\).

Answer:

\(u = 2.8\)