Question

what is m∠bcd? use the number pad to enter your answer in the box. m∠bcd = °

Explanation:

Step1: Find ∠CBD

A straight - line angle is 180°. Since ∠ABC + ∠CBD=180° and ∠ABC = 130°, then ∠CBD=180° - 130° = 50°.

Step2: Find ∠CDB

Since ∠CDE+∠CDB = 180° and ∠CDE = 122°, then ∠CDB=180° - 122° = 58°.

Step3: Use the angle - sum property of a triangle

In △BCD, the sum of the interior angles of a triangle is 180°. Let ∠BCD=x. Then x+∠CBD + ∠CDB=180°. Substitute ∠CBD = 50° and ∠CDB = 58° into the equation: x+50°+58°=180°.

Step4: Solve for ∠BCD

x=180°-(50° + 58°)=72°.

Answer:

72