Question

exercises
find the value of each variable.
1.
since diagonals bisect each other.
$3x = 12$ $4y = 8$
2.
since diagonals bisect each other. since diagonals are congruent and the triangle sides are equal:
$2y = 28$ $4x = 28$
note: rhombus (all equal sides)
3.
since the diagonals bisect angles in a rhombus: note: perpendicular $\
ightarrow 90^\circ$ use triangle angle sum:
$2x = 60^\circ$ $90^\circ + 60^\circ + 4y^\circ = 180^\circ$

Explanation:

Problem 1

Step1: Solve for \( x \)

Given \( 3x = 12 \), divide both sides by 3.
\( x=\frac{12}{3}=4 \)

Step2: Solve for \( y \)

Given \( 4y = 8 \), divide both sides by 4.
\( y=\frac{8}{4}=2 \)

Step1: Solve for \( y \)

Given \( 2y = 28 \), divide both sides by 2.
\( y=\frac{28}{2}=14 \)

Step2: Solve for \( x \)

Given \( 4x = 28 \), divide both sides by 4.
\( x=\frac{28}{4}=7 \)

Step1: Solve for \( x \)

Given \( 2x = 60^\circ \), divide both sides by 2.
\( x=\frac{60^\circ}{2}=30^\circ \)

Step2: Solve for \( y \)

Given \( 90^\circ + 60^\circ + 4y^\circ = 180^\circ \), first simplify the left - hand side: \( 150^\circ+4y^\circ = 180^\circ \). Then subtract \( 150^\circ \) from both sides: \( 4y^\circ=180^\circ - 150^\circ=30^\circ \). Finally, divide both sides by 4: \( y=\frac{30^\circ}{4}=7.5^\circ \)

Answer:

\( x = 4 \), \( y = 2 \)

Problem 2