Question

3.       In the figure, what is the measure of LABC:​

Answer 1

Answer

To find the value of the ∠ABC, first we should find the values of the other two angles marked with an unknown angles with some variables. So, first we should find the value of one of those angles.

The concept to be used this angle is the vertically opposite angles. This property says that, the two angles opposite to each other, when two lines intersect each other will always measure equal.

$\sf \dashrightarrow Vertically \: opposite \: angles \: measure \: same$

$\sf \dashrightarrow {(3x + 33)}^{\circ} = {(4x + 8)}^{\circ}$

$\sf \dashrightarrow 3x + 33 = 4x + 8$

$\sf \dashrightarrow 3x - 4x = 8 - 33$

$\sf \dashrightarrow -1x = -25$

$\sf \dashrightarrow 1x = 25$

$\sf \dashrightarrow x = 25$

Now, we will find the value of the angle on top of the mid-point.

$\sf \dashrightarrow 3x + 33$

$\sf \dashrightarrow 3(25) + 33$

$\sf \dashrightarrow 75 + 33$

$\sf \dashrightarrow {108}^{\circ}$

Now, we can find the value of ∠ABC.

Value of ∠ABC :

$\sf \dashrightarrow {108}^{\circ} + \angle{ABC} = {180}^{\circ}$

$\sf \dashrightarrow \angle{ABC} = 180 - 108$

$\sf \dashrightarrow \angle{ABC} = {72}^{\circ}$

Hence, the value of ∠ABC is 72°.