Find the unknown angle measures.

Drawing is not to scale.
$$
\begin{array}{l}
x=\square \
y=\square \
w=\square
\end{array}
$$

Question

Find the unknown angle measures.

Drawing is not to scale.
$$
\begin{array}{l}
x=\square \
y=\square \
w=\square
\end{array}
$$

Accepted Answer

∻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.⚹◊What is the relationship between the interior angles of the two intersecting triangles and the sum of the angles in a triangle⍭ Generate me a similar question◊

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