Question

ABCD is a rhombus with angle DAB = 56°. Determine angle DBC

Answer 1

Answer:

angle CAB = 34 degrees

Step-by-step explanation:

∠BOA = 90º (vertically opposite angle)

∠BA0 = 180 - 56 - 90 = 34º (Sum of angles in a triangle)

∠BCA = 56º (Isosceles triangle)

∠BAC = 180 - 56 - 56 = 68º (Sum of angles in a triangle)

∠CAB = ∠BAC - ∠BAO

∠CAB = 68 - 34 = 34º

∠CAB = 34º

Answer 2

Concept :

A rhombus is a trapezoid with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.

Given:

ABCD is a rhombus with angle $DAB = 56°.$

Find:

Determine angle DBC

Solution:

According to the problem,

$DAB = 56º \\BDC = 56º$

$CDB +DBC = 180º - (56+56)º = 68º$ (Isosceles triangle)

So, $DBC = 34$

Hence the angle DBC is $34$°

SPJ2