Question

what kind of triangle is △bcd? explain. a. right triangle; m∠2 = 90 b. acute triangle; m∠cdb = 180 - 130 = 50 and m∠2 = 180 - 70 - 50 = 60 c. obtuse triangle; m∠cdb = 180 - 70 = 110 d. isosceles triangle; m∠cdb = m∠2

Explanation:

Step1: Find measure of ∠CDB

Since an exterior - angle and its adjacent interior - angle are supplementary, if the exterior angle at D is 130°, then \(m\angle CDB=180 - 130=50^{\circ}\).

Step2: Find measure of ∠2

Using the angle - sum property of a triangle (\(m\angle C + m\angle CDB+m\angle 2 = 180^{\circ}\)), and given \(m\angle C = 70^{\circ}\) and \(m\angle CDB = 50^{\circ}\), we have \(m\angle 2=180-(70 + 50)=60^{\circ}\).

Step3: Classify the triangle

Since \(m\angle C = 70^{\circ}\), \(m\angle CDB = 50^{\circ}\), and \(m\angle 2 = 60^{\circ}\), all angles of \(\triangle BCD\) are less than 90°. So, it is an acute triangle.

Answer:

B. Acute triangle; \(m\angle CDB = 180 - 130 = 50\) and \(m\angle 2 = 180 - 70 - 50 = 60\)