Question

quadrilateral jklm is a rhombus. find the missing values. m∠1 = m∠2 = m∠3 = m∠klm =

Explanation:

Step1: Diagonals of rhombus are perpendicular

$m\angle3 = 90^{\circ}$

Step2: Use angle - sum in triangle

In the triangle with $42^{\circ}$ angle, $m\angle1=42^{\circ}$ (alternate interior angles for parallel sides of rhombus).

Step3: Find $m\angle2$

$m\angle2 = 42^{\circ}$ (properties of rhombus diagonals bisect angles).

Step4: Find $m\angle KLM$

$m\angle KLM=84^{\circ}$ (since $m\angle KLM = 2\times m\angle2$).

Answer:

$m\angle1 = 42^{\circ}$
$m\angle2 = 42^{\circ}$
$m\angle3 = 90^{\circ}$
$m\angle KLM = 84^{\circ}$