Question

The exterior angle ACD of a triangle ABC is 105º. If angle B = 70°, find A. Is angle ACD > angle A? Find angle ACB also. ​

Answer 1

$\huge\bf{Given::}$

The exterior angle ACD of a triangle ABC is 105º. If angle B = 70°, find A. Is angle ACD > angle A? Find angle ACB also.

$\huge\bf{Solution}$

Find A :

By using the formula of-

Exterior angle of the triangle is equal to the sum of öpposite ïnterior angles of the triangle.

Exterior angle = 150°

First opposite interior angle = 70°

Let the second interior angle be x

Second öpposite interior angle = x

Now,

$\bf{70° + x = 150°} \\ \\ \bf{x = 150° - 70°} \\ \\ \bf{x = 80°}$

So, the second interior angle = x = 80° = A

Is angle ACD > angle A? :

$\text{Angle A = 80°} \\\text{Angle ACD = 150° as shöwn in the figure} \\ \text{150° > 80°}\\ \text{True, angle ACD is greater than angle A}$

Find angle ACB :

By using the formula of-

Sum of all angles on straight line is equal to 180°

Let angle ACB be y

Angles on straight line are angle ACD (150°) and angle ACB (y)

Now,

$\bf{150° + y = 180°} \\ \\ \bf{y = 180° - 150°} \\ \\ \bf{y = 30°}$

So, angle ACB = y = 30°

Another method of finding angle ACB :

By using the formula of-

Sum of all interior angles in a triangle is equal to 180°

First Angle = angle ABC = 70°

Second angle = angle BAC = 80°

Let angle ACB be y

Third angle = angle ACB = y

Now,

$\bf{70° + 80° + y = 180°} \\ \\\bf{150° + y = 180°} \\ \\ \bf{y = 180° - 150°} \\ \\ \bf{y = 30°}$

So, angle ACB = y = 30°

$\huge\bf{More\: Info::}$

$\small{\text{Sum of all angles on a straight line = 180° }}\\\small{\text{Sum of all interior angles in a triangle = 180° }}\\\small{\text{Sum of all angles around a pöint = 360° }} \\ \small{\text{Sum of opposite interior angles of a triangle = Exterior angle of the triangle}} \\ \small{\text{Angles less than 90° are called acute angle}} \\\small{\text{Angles more than 90° are called obtuse angle} }\\ \small{\text{Angles of 90° are called right angle }} \\ \small{\text{Angles from 180° to 360° are called reflex angle } }\\\small{\text{Angle of 360°are called complete angle} }$

$\bf{Hope\:it \: helps}$