Question

find the value of angle s. you first need to find the value of x.
question 8
1 pts
find the value of angle d. you first need to find the value of x.

Explanation:

First Problem (Finding angle \( S \)):

Step1: Recall quadrilateral angle sum

The sum of interior angles in a quadrilateral is \( 360^\circ \). So, \( (10x - 4) + 94 + 85 + (17x - 4) = 360 \).

Step2: Combine like terms

\( 10x + 17x - 4 - 4 + 94 + 85 = 360 \)
\( 27x + 171 = 360 \).

Step3: Solve for \( x \)

\( 27x = 360 - 171 \)
\( 27x = 189 \)
\( x = \frac{189}{27} = 7 \).

Step4: Find angle \( S \)

Substitute \( x = 7 \) into \( 17x - 4 \):
\( 17(7) - 4 = 119 - 4 = 115 \).

Step1: Recall quadrilateral angle sum

The sum of interior angles in a quadrilateral is \( 360^\circ \). So, \( 74 + 100 + (8x + 10) + (17x + 1) = 360 \).

Step2: Combine like terms

\( 8x + 17x + 74 + 100 + 10 + 1 = 360 \)
\( 25x + 185 = 360 \).

Step3: Solve for \( x \)

\( 25x = 360 - 185 \)
\( 25x = 175 \)
\( x = \frac{175}{25} = 7 \).

Step4: Find angle \( D \)

Substitute \( x = 7 \) into \( 8x + 10 \):
\( 8(7) + 10 = 56 + 10 = 66 \).

Answer:

\( 115^\circ \)

Second Problem (Finding angle \( D \)):