Question

10 find the value of $x$ and $y$ in the isosceles trapezoid below.$(16n - 12)\degree$$(24m)\degree$ $(5n + 3)\degree$$n = \square$$m = \square$show hint

Explanation:

Step1: Use consecutive angles property

In an isosceles trapezoid, consecutive angles between the bases are supplementary, so:
$$(16n - 12) + (5n + 3) = 180$$

Step2: Simplify and solve for $n$

Combine like terms and isolate $n$:
$$21n - 9 = 180$$
$$21n = 189$$
$$n = \frac{189}{21} = 9$$

Step3: Use base angles property

Base angles of an isosceles trapezoid are equal, so:
$$24m = 5n + 3$$

Step4: Substitute $n=9$ and solve for $m$

Plug in $n=9$ and calculate $m$:
$$24m = 5(9) + 3 = 45 + 3 = 48$$
$$m = \frac{48}{24} = 2$$

Answer:

$n = 9$
$m = 2$