Question

what is the measure of angle bcd? 25° 40° 140° 155°

Explanation:

Step1: Find the measure of \(\angle ABD\)

Since \(\angle ABD + 146^{\circ}=180^{\circ}\) (linear - pair of angles), then \(\angle ABD = 180^{\circ}-146^{\circ}=34^{\circ}\).

Step2: Find the measure of \(\angle BDC\)

Since \(\angle BDC + 149^{\circ}=180^{\circ}\) (linear - pair of angles), then \(\angle BDC=180^{\circ}-149^{\circ}=31^{\circ}\).

Step3: Use the angle - sum property of a triangle

In \(\triangle BCD\), we know that the sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle BCD = x\).
We are given one angle in the triangle as \(25^{\circ}\) (from the parallel - line transversal property, assume the angle inside the triangle related to the \(25^{\circ}\) exterior angle).
Using the angle - sum formula for a triangle \(x + 31^{\circ}+34^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(31^{\circ}+34^{\circ}+25^{\circ})$$

$$x = 180^{\circ}-90^{\circ}$$

$$x = 140^{\circ}$$

Answer:

\(140^{\circ}\)