Question

In the diagram below of rhombus ABCD,mZC = 100.АB100°DCWhat is mZDBC?Your answer

Answer 1

A rhomus can be said to be a quadilateral with equal side lengths. A rhombus has equal opposite angles and the sum of interior angles of a rhombus sum up to 360 degrees.

Given:

m∠C = 100 degrees

Since opposite angles of a rhombus are equal, we have:

m∠A = m∠C

m∠B = m∠D

Since the interior angles of a rhombus sum up to 360 degrees, we have the equation:

m∠A + m∠C + m∠D + m∠B= 360

m∠A + m∠C + 2(m∠B) = 360

100 + 100 + 2(m∠B) = 360

200 + 2(m∠B) = 360

Subtract 200 from both sides:

200 - 200 + 2(m∠B) = 360 - 200

2(m∠B) = 160

Divide both sides by 2:

`\begin{gathered} (2(m\angle B))/(2)=(160)/(2) \\ \\ m\angle B\text{ = 80 degre}es \end{gathered}`

The diagonals of a rhombus bisect the vertex angles of the rhombus

We can see the DB is a diagonal, which divides the angle D and B into two equal parts.

Thus, to find m∠DBC, we have:

`\begin{gathered} m\angle\text{DBC = }(m\angle B)/(2) \\ \\ m\angle\text{DBC}=(80)/(2)=40\text{ degr}ees \end{gathered}`

Therefore, the measure of angle DBC is 40 degrees.

ANSWER:

m∠DBC = 40 degrees