In Delta mathrm{WXY}, overline{W Y} is extended through point mathrm{Y} to point mathrm{Z}, mathrm{m} angle Y W X=(2 x+9)^{circ}, mathrm{m} angle W X Y=(2 x+16)^{circ}, and mathrm{m} angle X Y Z=(8 x+1)^{circ}. Find mathrm{m} angle W X Y.

Question

Accepted Answer

Step:1 ：The problem involves a triangle and an extended line, forming an exterior angle. 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, ( angle YWZ = angle YWX + angle WXY ).Step:2 ：We can set up an equation using this relationship: ( (2x + 9) + (2x + 16) = (8x + 1) ).Step:3 ：Solving this equation gives us the value of ( x = 6 ).Step:4 ：Substituting ( x = 6 ) back into the expression for ( angle WXY ), we get ( angle WXY = 2x + 16 = 28 ).Step:5 ：Final Answer: The measure of ( angle WXY ) is ( boxed{28^{circ}} ).

Answer

Step: 1 ：The problem involves a triangle and an extended line, forming an exterior angle. 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, ( angle YWZ = angle YWX + angle WXY ).Step: 2 ：We can set up an equation using this relationship: ( (2x + 9) + (2x + 16) = (8x + 1) ).Step: 3 ：Solving this equation gives us the value of ( x = 6 ).Step: 4 ：Substituting ( x = 6 ) back into the expression for ( angle WXY ), we get ( angle WXY = 2x + 16 = 28 ).Step: 5 ：Final Answer: The measure of ( angle WXY ) is ( boxed{28^{circ}} ).

In $Δ WXY, \overset{―}{W Y}$ is extended through point $Y$ to point $Z$ , $m ∠ Y W X = (2 x + 9)^{\circ}$ , $m ∠ W X Y = (2 x + 16)^{\circ}$ , and $m ∠ X Y Z = (8 x + 1)^{\circ}$ . Find $m ∠ W X Y$ .

Answer

Popular Problems

In ΔWXY,WY― is extended through point Y to point Z, m∠YWX=(2x+9)∘, m∠WXY=(2x+16)∘, and m∠XYZ=(8x+1)∘. Find m∠WXY.

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Popular Problems

In $Δ WXY, \overset{―}{W Y}$ is extended through point $Y$ to point $Z$ , $m ∠ Y W X = (2 x + 9)^{\circ}$ , $m ∠ W X Y = (2 x + 16)^{\circ}$ , and $m ∠ X Y Z = (8 x + 1)^{\circ}$ . Find $m ∠ W X Y$ .