Question

draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.

Answer 1

So, $\angle ABD+\angle DBC=\angle ABC$

Step-by-step explanation:

Given;

Draw an $\angle ABC$ of measure $105$°

• Take a point $D$ which is perpendicular with point $B$
• And Join $BD$

So,

$\angle DBC=90$°

And $\angle ABD=\angle ABC-\angle DBC$

∴$\angle ABD=15$°

∴$\angle ABD+\angle DBC=105$

Then,

Therefore $\angle ABD+\angle DBC=\angle ABC$

Answer 2

Given that,

Angle ABC = 105°

We need to verify by measuring that  angle ABD + angle DBC = angle ABC

Firstly, we draw a line BC

Now, we take any fixed radius and draw an arc with center at B.

We mark the intersection point of the arc is D

Now, join the BD.

BD is the angle bisector of angle ABC.

So, angle DBC is 90°.

Now, use the protractor,

Put the center of the protractor on B and draw an angle ABC = 105°

We need to calculate the angle ABD

According to the figure,

$\angle ABC=\angle ABD+\angle DBC$

Put the value in to the formula

$105=\angle ABD+90$

$105-90=\angle ABD$

$\angle ABD=15^{0}$

So, $\angle ABD + \angle DBC = \angle ABC$

Hence, This is proved.