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Find the indicated measure in D ABCD. Provide a reason for each answer. Use correct symbol in your answer. MLABC = because

Find the indicated measure in D ABCD. Provide a reason for each answer. Use correct symbol in your answer. MLABC = because

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem Statement Find the indicated measure in parallelogram \( \square ABCD \). Provide a reason for each answer. Use the correct symbol in your answer. \[ m \angle ABC = \_\_\_\_\_\_\_ \; \text{because} \; \_\_\_\_\_\_\_ \] ### Diagram Description The diagram provided is of a parallelogram \( \square ABCD \). The diagram includes the following details: - \( \angle DAB \) is labeled as 120 degrees. - \( \angle ADC \) is labeled as 43 degrees. - Side \( AB \) is 16 units in length. - Diagonal \( AC \) is labeled with segments \( AE \) and \( EC \) measuring 8 units each. - Diagonal \( BD \) is labeled with segments \( BE \) and \( ED \) measuring 7 units each. - Intersection point \( E \). ### Answer: Since the sum of the angles in any parallelogram is \( 360^\circ \) and opposite angles are equal, the measure of \( \angle ABC \): \[ m \angle ABC = 43^\circ \; \text{because} \; (\text{opposite angles in a parallelogram are equal}). \]
Transcribed Image Text:### Problem Statement Find the indicated measure in parallelogram \( \square ABCD \). Provide a reason for each answer. Use the correct symbol in your answer. \[ m \angle ABC = \_\_\_\_\_\_\_ \; \text{because} \; \_\_\_\_\_\_\_ \] ### Diagram Description The diagram provided is of a parallelogram \( \square ABCD \). The diagram includes the following details: - \( \angle DAB \) is labeled as 120 degrees. - \( \angle ADC \) is labeled as 43 degrees. - Side \( AB \) is 16 units in length. - Diagonal \( AC \) is labeled with segments \( AE \) and \( EC \) measuring 8 units each. - Diagonal \( BD \) is labeled with segments \( BE \) and \( ED \) measuring 7 units each. - Intersection point \( E \). ### Answer: Since the sum of the angles in any parallelogram is \( 360^\circ \) and opposite angles are equal, the measure of \( \angle ABC \): \[ m \angle ABC = 43^\circ \; \text{because} \; (\text{opposite angles in a parallelogram are equal}). \]
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