Question

Use the figure at the right.Given:CE//AB,find the measurement of the following angles




what's the answer the answer in this question pleaseee​

Answer 1

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$1)\\\angle ACD = 90^0\\\\</p><p>2)\\\angle CAB = 90^0\\\\</p><p>3)\\\angle CDB = (360 - 90 - 90 - 54)^0 = 126^0\\\\</p><p>4)\\\angle EDB = 54^0\\\\</p><p>5)\\\angle CDE = 180^0\\\\ \:$

Answer 2

The measures of the angles are as follows:

m∠ACD= 90°

m∠CAB= 90°

m∠CDB= 126°

m∠EDB= 54°

m∠CDE= 180°

Step-by-step explanation:

Given:

line CE ║ line AB

m∠DBA= 54°

To find:

measures of the angles given

Solution:

m∠CAB= 90°...........(perpendicular sign given in the figure)

It is gevn that line CE ║ line AB

m∠CAB & m∠ACD are in interior pair

∴ m∠CAB + m∠ACD=180°........(angles in interior pair are supplementary)

∴ 90° + m∠ACD=180°

∴ m∠ACD=180°-90°

∴ m∠ACD=90°

Consider quadrilateral CDBA

m∠ACD=90°,  m∠DBA= 54°, m∠CAB= 90°

∠ACD+ ∠CDB+ ∠DBA+ ∠CAB = 360°.....(sum of all angles of a

                                                                               quadrilateral is 360°)

∴ 90°+ ∠CDB+ 54°+ 90°=360°

∴∠CDB= 360°- 234°

∴m∠CDB= 126°

The angles EDB & CDB are in linear pair

∴m∠EDB + m∠CDB= 180°

∴m∠EDB + 126°=180°

∴m∠EDB= 180°-126°

∴ m∠EDB= 54°

The angles formed on CDE are in linear pair

Therefore, the measure of angle CDE will be 180°

∴ m∠CDE= 180°

Hence, the measures of angles are m∠ACD= 90°; m∠CAB= 90°; m∠CDB= 126°; m∠EDB= 54°; m∠CDE= 180°