Question

if AD and BD are bisector of angle CAB and angle CBA, respectively find the sum of angles x and y ​

Answer 1

Answer:

Step-by-step explanation:

The picture in the attached figure

Step 1

we know that

It is given that AD and BD are bisectors of ∠CAB and ∠CBA respectively.

Therefore,

x = ∠CAB/2 -----> equation 1

y = ∠CBA/2 -----> equation 2

Step 2

In triangle ABC,

∠CAB + ∠CBA + ∠ACB = 180° ----> [The sum of all three angles of a triangle is 180°]

∠CAB + ∠CBA + 110° = 180°

∠CAB + ∠CBA = 180° - 110°

∠CAB + ∠CBA = 70° ------> divide by 2 both sides

∠CAB/2 + ∠CBA/2 = 70/2 -------> equation 3

substitute equation 1 and equation 2 in equation 3

x+y=35

Hence,

the answer is

x+y =35°

⇒ x + y = 35° ...[From equation (1) and (2)]

HOPE IT HELPS

Answer 2

The sum of angles;

$\bf \red{ \angle \: x + \angle \: y = {40}^{ \circ}}$

Step-by-step explanation:

Given:

• A triangle ABC.
• $\angle \: ACB = {100}^{ \circ}$
• AD and BD are the angle bisector of $\angle \: CAB$ and $\angle \: CBA$ respectively.

To find:

• Find the sum of angles x and y.

Solution:

Theorem to be used:

Angle sum property of triangle:

• The sum of interior angles of triangle is 180°.

Step 1:

Find the sum of angles; i.e.$\angle \: CAB$ and $\angle \: CBA$.

According to angle sum property of triangle.

$\angle \: CAB + \angle \: CBA + \angle \: ACB= {180}^{ \circ}$

or

$\angle \: CAB + \angle \: CBA + {100}^{ \circ}= {180}^{ \circ}$

or

$\bf \angle \: CAB + \angle \: CBA = {80}^{ \circ}...eq1$

Step 2:

Find the sum of angles x and y.

As AD and BD are angle bisectors.

So,

$2x = \angle \: CAB$

and

$2y = \angle \: CBA$

put these values in eq1

$2x + 2y = {80}^{ \circ}$

or

$\bf x + y = {40}^{ \circ}$

Thus,

Sum of angle x and angle y is 40°.

$\bf \angle \: x + \angle \: y = {40}^{ \circ}$

Learn more:

1) in the given figure . find angle RQU.

https://brainly.in/question/7969230

2) In the given figure, if x°, y °and z°are exterior angles of triangle ABC, then find the value of xº + y + zº.

Please don...

https://brainly.in/question/45802677

#SPJ3