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Karo-lina-s [1.5K]
3 years ago
13

HELP PLEASE!!! 10 PTS!!

Mathematics
1 answer:
allsm [11]3 years ago
6 0

Answer:

m∠DEC = 78°

Step-by-step explanation:

Given information: AC = AD, AB⊥BD, m∠DAC = 44° and CE bisects ∠ACD.

If two sides of a triangles are congruent then the opposite angles of congruent sides are congruent.

AC = AD                 (Given)

\angle ADC\cong \angle ACD

m\angle ADC=m\angle ACD

According to the angle sum property, the sum of interior angles of a triangle is 180°.

m\angle ADC+m\angle ACD+m\angle DAC=180

m\angle ACD+m\angle ACD+44=180

2m\angle ACD=180-44

2m\angle ACD=136

Divide both sides by 2.

m\angle ACD=68

CE bisects ∠ACD.

m\angle ACE=m\angle DCE=\dfrac{\angle ACD}{2}

m\angle ACE=m\angle DCE=\dfrac{68}{2}

m\angle ACE=m\angle DCE=34

Use angle sum property in triangle CDE,

m\angle CDE+m\angle DCE+m\angle DEC=180

68+34+m\angle DEC=180

68+34+m\angle DEC=180

102+m\angle DEC=180

Subtract 102 from both sides.

m\angle DEC=180-102

m\angle DEC=78

Therefore, the measure of angle DEC is 78°.

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