Question

angle ABD and angle BDC are complementary, find the measures of both angles of each angle if Angle ABD=(x-30)° and angle BDC=2x°.​

Answer 1

$we \: know \: that, \\ sum \: of \: complementary \: angles \: \\ is \: 90° \\ \\ = > (x - 30) + 2x = 90° \\ \\ = > x - 30 + 2x = 90 \\ \\ = > 3x - 30 = 90° \\ \\ = > 3x = 90 + 30 \\ \\ = > x = \frac{120}{3} \\ \\ = > x = 40° \\ \\ angle \: ABD = (x - 30)° \\ = > 40 - 30 \\ = > 10° \\ \\ angle \: BDC = 2x \\ = > 2 \times 40 \\ = > 80°$

Answer 2

Answer:

$\large\boxed{\star\:\:\:\angle ABD=10\:degrees\:and\:\angle BDC=80\:degrees\:\:\:\star}$

Step-by-step explanation:

✦Given:-

∠ABD=(x-30) and ∠BDC=2x.

✦To Find:-

∠ABD and ∠BDC.

✦We Know That:-

  →Complementary angles are two angles that have a sum of 90°.

✦Solution:-

  ∠ABD+∠BDC=90°

⇒x-30°+2x=90°

⇒3x=90°+30°

⇒3x=120°

⇒x=$\frac{120}{30}$

⇒x=40°

Now,

∠ABD=x-30°

∠ABD=40°-30°

→∠ABD=10°

∠BDC=2x

∠BDC=2×(40)°

→∠BDC=80°