Math Problem Statement

Help me answer this question

In the figure below not drawn to scale, ABCE is a parallelogram. Find angle ADC.

Solution

We are given a parallelogram ABCEABCE, and we need to find the measure of ADC\angle ADC.

Step-by-Step Solution:

  1. Parallelogram Properties:
    In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Also, adjacent angles on a straight line sum to 180°.

  2. Identify EAB\angle EAB:

    • We are given that A=47\angle A = 47^\circ and B=65\angle B = 65^\circ. Since ABCEABCE is a parallelogram, the interior angles EAB\angle EAB and ABC\angle ABC are supplementary: EAB+ABC=180\angle EAB + \angle ABC = 180^\circ So: 47+65=11247^\circ + 65^\circ = 112^\circ Therefore, EAB\angle EAB and BEC\angle BEC sum up to ( 180^\circ ( to fill

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallelogram Properties
Angle Relationships

Formulas

Sum of interior angles of a parallelogram is 360°
Adjacent angles on a straight line sum to 180°

Theorems

Opposite angles of a parallelogram are equal
Consecutive angles in a parallelogram are supplementary

Suitable Grade Level

Grades 8-10