Question

in quadrilateral abcd, m∠b = 75°, determine m∠d. enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is \(180^\circ\). So, \(\angle B\) and \(\angle D\) are opposite angles.

Step2: Calculate \(m\angle D\)

Given \(m\angle B = 75^\circ\), using the property \(m\angle B + m\angle D=180^\circ\), we solve for \(m\angle D\):
\(m\angle D = 180^\circ - m\angle B\)
Substitute \(m\angle B = 75^\circ\) into the formula:
\(m\angle D = 180 - 75 = 105\)

Answer:

105