Question

In ΔWXY, m, angle, W, equals, left parenthesis, 4, x, plus, 11, right parenthesis, degreesm∠W=(4x+11)
∘
, m, angle, X, equals, left parenthesis, 2, x, minus, 17, right parenthesis, degreesm∠X=(2x−17)
∘
, and m, angle, Y, equals, left parenthesis, 5, x, plus, 10, right parenthesis, degreesm∠Y=(5x+10)
∘
. Find m, angle, Y, .m∠Y.

Answer 1

In triangle \( \Delta WXY \), the sum of the interior angles is \( 180^\circ \). Given the measures of the angles as:

\[
m\angle W = (4x + 11)^\circ,
\]
\[
m\angle X = (2x - 17)^\circ,
\]
\[
m\angle Y = (5x + 10)^\circ,
\]

we can set up the equation:

\[
m\angle W + m\angle X + m\angle Y = 180^\circ.
\]

Substituting the expressions for the angles, we have:

\[
(4x + 11) + (2x - 17) + (5x + 10) = 180.
\]

Now, simplifying the left-hand side:

\[
4x + 11 + 2x - 17 + 5x + 10 = 180.
\]
\[
(4x + 2x + 5x) + (11 - 17 + 10) = 180,
\]
\[
11x + 4 = 180.
\]

Next, we solve for \( x \):

\[
11x = 180 - 4,
\]
\[
11x = 176,
\]
\[
x = \frac{176}{11} = 16.
\]

Now that we have \( x = 16 \), we can find \( m\angle Y \):

\[
m\angle Y = 5x + 10 = 5(16) + 10 = 80 + 10 = 90.
\]

Thus, the measure of angle \( Y \) is:

\[
\boxed{90}.
\]