With the angles given in the triangle, the missing angles on the image are:
1.) m∠ECD = 136°
2.) m∠EBA = 11°
3.) m∠CDE = 22°
4.) m∠EAB = 22°
5.) m∠CED = 22°
6.) m∠AEB = 147°
7.) m∠DEB = 11°
8.) m∠CBA = 22°
9.) m∠EDB = 158°
10.) m∠DBE = 11°
Step-by-step explanation:
Segment ED ∥ segment AB
∠CED ≅ ∠CDE
m∠CAB = 22°
m∠ABE = 11°
m∠ACB = 136°
1.) m∠ECD
The m∠ECD is the same that the m∠ACB, then:
m∠ECD = m∠ACB
m∠ECD = 136°
2.) m∠EBA
The m∠EBA is the same that the m∠ABE, then:
m∠EBA = m∠ABE
m∠EBA = 11°
3.) m∠CDE
It is given that:
∠CED ≅ ∠CDE, then m∠CED = m∠CDE
And because of the segment ED ∥ segment AB, the ∠CED must be congruent with ∠CAB, because the corresponding angles in parallel lines (ED and AB) cut by a secant (CA) must be congruent, then:
m∠CED = m∠CAB
m∠CED = 22° (Answer part 5)
m∠CED = m∠CDE
22° = m∠CDE
m∠CDE = 22°
4.) m∠EAB
The m∠EAB is the same that the m∠CAB, then:
m∠EAB = m∠CAB
m∠EAB = 22°
5.) m∠CED
See Explanation in part 3:
m∠CED = 22°
6.) m∠AEB
In triangle AEB:
m∠EAB = 22°
m∠ABE = 11°
m∠AEB = ?
The sum of the measurements of the interior angles of any triangle must be equal to 180°, then:
m∠EAB + m∠ABE + m∠AEB = 180°
Replacing the known values in the equation above:
22° + 11° + m∠AEB = 180°
Adding like terms on the left side of the equation:
33° + m∠AEB = 180°
Solving for m∠AEB: Subtracting 33° both sides of the equation:
33° + m∠AEB - 33° = 180° - 33°
Subtracting:
m∠AEB = 147°
7.) m∠DEB
Because of the segment ED // segment AB, the <DEB must be congruent with <ABE, because the alternate interior angles in parallel lines (ED and AB) cut by a secant (BE) must be congruent, then:
m<DEB = m<ABE
m<DEB = 11°
8.) m∠CBA
Because of the segment ED // segment AB, the <CBA must be congruent with <CDE, because the corresponding angles in parallel lines (ED and AB) cut by a secant (BC) must be congruent, then:
m<CBA = m<CDE (=22°, see part 3)
m<CBA = 22°
9.) m∠EDB
According with the figure, and because BC is a straight line, the sum of the measurements of the <CDE and <EDB must be equal to 180°, then:
m<CDE + m<EDB = 180°
By part 3 we know that m<CDE=22°. Replacing this value in the equation above:
22° + m<EDB = 180°
Solving for m<EDB: Subtracting 22° both sides of the equation:
22° + m<EDB - 22° = 180° - 22°
m<EDB = 158°
10.) m∠DBE
In triangle DBE:
m∠EDB = 158° (see part 9)
m∠DEB = 11° (see part 7)
m∠DEB = ?
The sum of the measurements of the interior angles of any triangle must be equal to 180°, then:
m∠EDB + m∠DEB + m∠DEB = 180°
Replacing the known values in the equation above:
158° + 11° + m∠DEB = 180°
Adding like terms on the left side of the equation:
169° + m∠DEB = 180°
Solving for m∠DEB: Subtracting 169° both sides of the equation:
169° + m∠DEB - 169° = 180° - 169°
Subtracting:
m∠DEB = 11°
