Question

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Answer 1

QUESTION:

TWO _______ ARE SAID TO FORM LINEAR PAIR OF THE ANGLES IF THEIR COMMON ARMS ARE TWO OPPOSITE RAYS.

ANSWER:

TWO ADJACENT ANGLES ARE SAID TO FORM LINEAR PAIR OF THE ANGLES IF THEIR COMMON ARMS ARE TWO OPPOSITE RAYS.

GIVEN:

TWO ARMS ARE OPPOSITE.

EXPLANATION:

As the two arms are opposite they form 180° between each other and hence they form the linear pairs because they lie in the same straight line. In the diagram A and B are the two lines having 180° between them.

$\pink{ \boxed{ \theta_1 + \theta _2 = 180 \degree}}$

NOTE : REFER ATTACHMENT FOR DIAGRAM.

Answer 2

Let the two angles be equal to x. Since they are equal we assume both of them to be x.

So according to angle sum property of triangle, the sum of all the interior angles of a triangle sum up to 180°.

=> Angle 1 + Angle 2 + Angle 3 = 180°

=> x + x + 80° = 180°

=> 2x + 80° = 180°

=> 2x = 180° - 80°

=> 2x = 100°

=> x = 100° / 2

=> x = 50°

Hence the angle measure of the two equal angles are 50°.