Answer:
The measure of angle AED is 173°
Step-by-step explanation:
Given
The figure above
Required
Calculate <AED
To calculate <AED, we follow the highlighted steps.
1. Calculate angle DEC in triangle DEC.
The angles in ∆DEC are <DEC, <ECD and <CDE where
<ECD = 37° and <CDE = 96°
THE SUM OF ANGLES IN A TRIANGLE IS 180°.
i.e.
<DEC + <ECD + <CDE = 180°
By substituting <ECD = 37° and <CDE = 96°, we have
<DEC + 37° + 96° = 180°
<DEC + 133° = 180°
<DEC = 180° - 133°
<DEC = 47°
2. Calculate angle CEB in triangle CEB.
The angles in ∆CEB are <CEB, <EBC and <BCE where
<EBC = 73° and <BCE = 79°
THE SUM OF ANGLES IN A TRIANGLE IS 180°.
i.e.
<CEB + <EBC + <BCE = 180°
By substituting <EBC = 73° and <BCE = 79°, we have
<CEB + 73° + 79° = 180°
<CEB + 152° = 180°
<CEB = 180° - 152°
<CEB = 28°
3. Calculate <AED
This calculated by taking the sum of angles are point E.
The angles at point E are <AED, <AEB, <CEB and <DEC.
Where <AEB = 112°, <CEB = 28°, <DEC = 47°
Recall that sum of angles at a point is 360°.
So,
<AED + <AEB + <CEB + <DEC = 360
By substituting <AEB = 112°, <CEB = 28°, <DEC = 47°, we have
<AED + 112° + 28° + 47° = 360
<AED + 187° = 360°
<AED = 360° - 187°
<AED = 173°.
Hence, the measure of angle AED is 173°
