А Triangles ACD and BCD are isosceles. Angle BAC has a
measure of 33 degrees and angle BDC has a measure of 35
degrees. Find the measure of angle ABD.
B

The measure of angle ABD is equal to and this can be determined by using the properties of the triangle.

Given :

Given that side .

Given that side .

according to the reflexive property.

So, according to the above statements triangle DAB is congruent to triangle CAB by the SSS postulate.

Now according to CPCTC Angle BAD is congruent to angle BAC.

  (according to the angle addition postulate)

Now, according to the sum of the interior angle of the triangle theorem:

Therefore, the angle ABD and angle ABC are congruent according to the CPCTC.

Now, according to the definition of congruency angle ABD is equal to angle ABC.

Now, again according to the sum of angles at a point:

For more information, refer to the link given below:

link

The measure of angle ∠ABD is 125°

Step-by-step explanation:

The given parameters are;

Triangle of ΔACD = Isosceles triangle

Triangle of ΔBCD = Isosceles triangle

m∠BAC = 33°

m∠BDC = 35°

Whereby ΔBCD and ΔACD have their vertex in the same direction, we can have;

≅ Given sides legs of triangle ACD

≅ Given sides legs of triangle BCD

≅ Reflexive property

∴ ΔDAB ≅ ΔCAB  by SSS (Side-Side-Side) congruency rule

m∠BAC ≅ m∠BAD CPCTC (Congruent Parts of Congruent Triangles are Congruent)

∴ m∠BAC ≅ m∠BAD = 33° Definition of congruency

m∠BAC + m∠BAD = 33° + 33° = 66° = m∠DAC Angle addition postulate

m∠ADC = m∠ACD = (180 - m∠DAC)/2 = (180 - 66)/2 = 57° Base angles of an isosceles triangle

∴ m∠ADC = m∠ACD = 57°

m∠BDC = 35° = m∠BCD Base angles of isosceles triangle ΔBCD

m∠BCD + m∠DBC + m∠BCD = 180° Sum of the interior angles of a triangle theorem

m∠DBC = 180° - (m∠BCD +  m∠BCD) = 180° - (35° +  35°) = 110°

m∠DBC = 110°

∴ m∠ABD ≅ m∠ABC CPCTC

m∠ABD = m∠ABC Definition of congruency

m∠DBC + m∠ABD + m∠ABC = 360° Sum of angles at a point

m∠DBC + m∠ABD + m∠ABD = 360°

m∠DBC + 2 × m∠ABD = 360°

110° + 2 × m∠ABD = 360°

2 × m∠ABD = 360° - 110° = 250°

2 × m∠ABD = 250°

m∠ABD = 250°/2 = 125°

m∠ABD = 125°.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

hey seth! : )

i’m not 100% sure, but i think it’s b

hope this ya : p

miss u!

- nicole