Question

in the given figure the measure of angle ABC is​

Answer 1

Answer:

x + 20 + 100 = 180 (sum of angles in a ∆)

=) x + 120 = 180

=) x = 180 - 120

=) x = ABC = 60°

hope it's gonna help you...☺

Answer 2

The measure of the angle ABC is 80°

Step-by-step explanation:

Given:

In the figure, ∠AOD=20°, exterior ∠C= 100°

To find:

m∠ABC

Solution:

In the figure, angles AOD and BOC will be equal

∠AOD= ∠BOC..........(vertically opposite angles)

∴ ∠AOD= ∠BOC = 20°......(i)

Now, exterior angle C and angle DCB are in linear pair

∴ exterior ∠C+ ∠DCB= 180°........(angles in linear pair have a sum of 180°)

∴ 100°+ ∠DCB = 180°

∴ ∠DCB = 180°-100°

∴ ∠DCB = 80°..........(ii)

Now, in ΔBOC, ∠BOC= 20°, ∠DCB= 80°

∠OBC+ ∠BOC+ ∠OCB=180°.....(sum of angles of a triangle is 180°)

Now, ∠OBC= ∠ABC & ∠OCB=∠DCB....(angles in same line)

∴ ∠ABC+ 20°+80°=180°.....[from (i) & (ii)]

∴ ∠ABC+100°= 180°

∴ ∠ABC= 180°-100°

∴ ∠ABC= 80°

Thus the measure of angle ABC is 80°

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