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2 years ago

PLEASEEEE HELPPPP ASAPPPP

Mathematics

1 answer:

adelina 88 [10]2 years ago

6 0

Answer:

x ≈ 7.1

Step-by-step explanation:

Using the cosine ratio in the right triangle.

cos27° = $\frac{adjacent}{hypotenuse}$ = $\frac{KL}{KM}$ = $\frac{6.3}{X}$ ( multiply both sides by x )

x × cos27° = 6.3 ( divide both sides by cos27° )

x = $\frac{6.3}{cos27}$ ≈ 7.1 ( to the nearest tenth )

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Answer:

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Step-by-step explanation:

It is important to remember that, by definition, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

In this case we can idenfity that the angle $17x$ is an exterior angle of the triangle QRT. Then:

$17x=\angle RTQ+\angle TQR$

Where:

$\angle RTQ=2x\\\\\angle TQR=48\°$

Substituting values and solving for "x", we get:

$17x=2x+48\\\\17x-2x=48\\\\15x=48\\\\x=3.2$

Then:

$17x=17(3.2)=54.4\°\\\\\\\angle RTQ=2(3.2)=6.4\°$

The sum of the interior angles of a triangle is 180°, therefore:

$\angle QRT+\angle RTQ+\angle TQR=180$

Solving for $\angle QRT$ , we get:

$\angle QRT=180-48-6.4=125.6\°$

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