Question

HELP PLEASE!!! 10 PTS!!


AC = AD, AB perpendicular to BD, m angle DAC = 44 degrees and CE bisects angle ACD. Find m angle DEC.


Angle DEC = ______

Answer 1

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°.