Question

Math

Posted 4 months ago

```
Find the unknown angle measures.
Drawing is not to scale.
$\begin{array}{l}
x=\square \\
y=\square \\
w=\square
\end{array}$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Identify the known angles in the left triangle. The angles are 81 degrees and 42 degrees

step 2

Use the fact that the sum of angles in a triangle is 180 degrees to find the unknown angle in the left triangle

step 3

Calculate the unknown angle: $180^\circ - 81^\circ - 42^\circ = 57^\circ$. Therefore, the unknown angle in the left triangle is 57 degrees

step 4

Identify the known angles in the right triangle. The angles are 100 degrees and y degrees

step 5

Use the fact that the sum of angles in a triangle is 180 degrees to find the unknown angle in the right triangle

step 6

Calculate the unknown angle: $180^\circ - 100^\circ - y^\circ = 80^\circ - y^\circ$. Therefore, the unknown angle in the right triangle is $80^\circ - y^\circ$

step 7

Since the two triangles share a common angle labeled as x degrees, we know that $x = 57^\circ$

step 8

The angle w is formed by the intersection of the two triangles. Since the sum of angles around a point is 360 degrees, we can find w by subtracting the known angles from 360 degrees

step 9

Calculate w: $360^\circ - 81^\circ - 42^\circ - 100^\circ = 137^\circ$. Therefore, $w = 137^\circ$

step 10

The angle y can be found by using the fact that the sum of angles in the right triangle is 180 degrees. Since we already know that $x = 57^\circ$, we can use this to find y

step 11

Calculate y: $180^\circ - 100^\circ - 57^\circ = 23^\circ$. Therefore, $y = 23^\circ$

Answer

$x = 57^\circ$, $y = 23^\circ$, $w = 137^\circ$

Key Concept

Sum of angles in a triangle

Explanation

The sum of the angles in any triangle is always 180 degrees. This property allows us to find unknown angles when the other angles are known.

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