Exercise 73 Page 397

We want to find the value of $x$ in the given rhombus.

Recall that if a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

If the parallelogram is a rhombus, then the diagonals are perpendicular. Notice that the right angle and the angles of measures

(2 x + 8)^{\circ}

and

(4 x + 10)^{\circ}

are the three angles of a triangle. By the Triangle Angle-Sum Theorem, we know they add to

180 .

90 + 2 x + 8 + 4 x + 10 = 180

Let's solve this equation to find

x .

90 + 2 x + 8 + 4 x + 10 = 180

▼

Solve for

x

Add terms

6 x + 108 = 180

$LHS - 108 = RHS - 108$

6 x = 72

$LHS / 6 = RHS / 6$

x = 12