Question

∠ace is a straight angle. write and solve an equation to find the unknown angle measure.
measure of ∠bcd is ______.

Explanation:

Step1: Recall straight angle property

A straight angle measures \(180^\circ\). So, \(\angle ACE = 180^\circ\), and \(\angle ACB + \angle BCD + \angle DCE = 180^\circ\). Given \(\angle ACB = 51^\circ\), \(\angle BCD = x^\circ\), \(\angle DCE = 43^\circ\). The equation is \(51 + x + 43 = 180\).

Step2: Simplify and solve for \(x\)

Combine like terms: \(94 + x = 180\). Subtract 94 from both sides: \(x = 180 - 94\). \(x = 86\).

Answer:

The measure of \(\angle BCD\) is \(86^\circ\).