Question

find the measure of the unknown angles

Answer 1

* To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.

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Answer 2

Given:

Two figures are given with some given angle x and y

To find:

The measure of the unknown angles

Step-by-step explanation:

• Let the points are A B and C in this given figure
• At point, A of the triangle exterior angle of the triangle is equal to the

        the interior angle which is equal to x  [by the vertically

         opposite angle]

         ∴ ∠BAC =  x

• At point B of the triangle also exterior angle of the triangle is equal to the interior angle which is equal to x  [by the vertically opposite angle]

• ∴ ∠ABC =  x

• At point C angle Y is equal to Angle X by the property of vertically  opposite angle

        ∴ ∠ACB = x

• By the sum of angle of triangle property

        ∠ACB+∠ABC+∠BAC = 180°

        ∴                       x+x+x = 180°

                                       3x = 180°

                                         x = 60°

           As all the angles are 60° So, It is an equilateral triangle

• In part b

• 2x +3x +x = 180 °     [angle of a straight line is 180°]

                   6x = 180 °

                   x  =  30°