In ΔWXY, start overline, W, Y, end overlineWY is extended through point Y to point Z, m, angle, Y, W, X, equals, left bracket, 2, x, plus, 9, right bracket, degreesm∠YWX=(2x+9)∘, m, angle, W, X, Y, equals, left bracket, 2, x, plus, 16, right bracket, degreesm∠WXY=(2x+16)∘, and m, angle, X, Y, Z, equals, left bracket, 8, x, plus, 1, right bracket, degreesm∠XYZ=(8x+1)∘. Find m, angle, W, X, Y, .m∠WXY
Since ∠WXY and ∠YWX are adjacent angles, they form a linear pair. Therefore, their sum is equal to 180 degrees.
(2x + 9) + (2x + 16) = 180
4x + 25 = 180
4x = 155
x = 38.75
m∠WXY = 2(38.75) + 9 = 86.5 degrees.
To find the measure of angle WXY (m∠WXY), we need to use the information given in the problem. Let's break it down step by step.
1. We know that the angle YWX has a measure of (2x + 9) degrees.
2. The angle WXY has a measure of (2x + 16) degrees.
3. The angle XYZ has a measure of (8x + 1) degrees.
Since we are looking for the measure of angle WXY, we need to focus on the second angle given.
m∠WXY = (2x + 16) degrees
Now, we have to find the value of x in order to determine the measure of angle WXY.
To do this, we can set up an equation by equating the sum of the three angles within the triangle to 180 degrees, as the angles of a triangle add up to 180 degrees.
(2x + 9) + (2x + 16) + (8x + 1) = 180
Now, solve this equation to find the value of x.
Combine like terms: 2x + 9 + 2x + 16 + 8x + 1 = 180
12x + 26 = 180
Subtract 26 from both sides: 12x = 154
Divide both sides by 12: x = 154/12
Simplify: x = 12.83
Now that we have found the value of x, we can substitute it back into the equation for angle WXY to find its measure.
m∠WXY = (2x + 16)
m∠WXY = (2 * 12.83 + 16)
m∠WXY = 41.66
Therefore, the measure of angle WXY (m∠WXY) is approximately 41.66 degrees.
To find the measure of angle WXY (m∠WXY), we need to set up an equation using the given information:
m∠WXY = (2x + 16)°
Since we know m∠WXY is a triangle angle and angles in a triangle add up to 180°, we can set up the following equation:
m∠WXY + m∠YWX + m∠XYZ = 180°
Substituting the given values:
(2x + 16)° + (2x + 9)° + (8x + 1)° = 180°
Now, we solve for x:
2x + 16 + 2x + 9 + 8x + 1 = 180
12x + 26 = 180
12x = 180 - 26
12x = 154
x = 154/12
x ≈ 12.83
To find m∠WXY, substitute the value of x back into the equation:
m∠WXY = (2x + 16)°
m∠WXY = 2(12.83) + 16
m∠WXY ≈ 25.66 + 16
m∠WXY ≈ 41.66° (rounded to two decimal places)
Therefore, the measure of angle WXY (m∠WXY) is approximately 41.66°.