If line uw bisects angle tuv,, m angle tue = (13x-5) and angle wuv = (7x+31) find the value of x

Mathematics

1 answer:

scZoUnD [109]3 years ago

4 0

The value of x will be 6

Explanation

According to the below diagram, UW is the angle bisector of ∠TUV

That means, $\angle TUW = \angle WUV$

Given that, $\angle TUW = 13x-5$ and $\angle WUV= 7x+31$

So, the equation will be......

$13x-5=7x+31\\ \\ 13x-7x=31+5\\ \\ 6x=36\\ \\ x=\frac{36}{6}=6$

So, the value of x will be 6.

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5. To get to the library from his house, Robert biked 6 kilometers due east and then

AURORKA [14]

Answer:

24 kilometers.

Step-by-step explanation:

The shortest path between two points is a straight segment that connects the two points.

Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.

The two shorter segments are the two legs, and
The longer segment that joins the library and the house is the hypotenuse.

The length of the hypotenuse can be found with the Pythagorean Theorem.

$\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{Leg 1})^{2} + (\text{Leg 2})^{2}}\\&= \sqrt{6^{2} + 8^{2}}\\&= \sqrt{36 + 64} \\&= \sqrt{100}\\&= \rm 10\;km\end{aligned}$ .