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:
[tex]\begin{gathered} \frac{2(m\angle B)}{2}=\frac{160}{2} \\ \\ m\angle B\text{ = 80 degre}es \end{gathered}[/tex]
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:
[tex]\begin{gathered} m\angle\text{DBC = }\frac{m\angle B}{2} \\ \\ m\angle\text{DBC}=\frac{80}{2}=40\text{ degr}ees \end{gathered}[/tex]
Therefore, the measure of angle DBC is 40 degrees.
ANSWER:
m∠DBC = 40 degrees
