Question 77 The sum of two vertically opposite angles is 166- - Find each of the angles-

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Standard VII

Mathematics

Angle Sum Property

Question 77 T...

Question

Question 77

The sum of two vertically opposite angles is $166^{\circ}$ . Find each of the angles.

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Solution

When two lines intersect, then vertically opposite angles so formed are equal. Let x be the measure of each vertically opposite angles,
Then, $x + x = 166^{\circ} \Rightarrow 2 x = 166^{\circ} \Rightarrow x = \frac{166^{\circ}}{2} = 83^{\circ}$
So, the measure of each angle is $83^{\circ}$ .

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Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

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Angle Sum Property

Standard VII Mathematics

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Question 77 The sum of two vertically opposite angles is 166∘. Find each of the angles.

When two lines intersect, then vertically opposite angles so formed are equal. Let x be the measure of each vertically opposite angles, Then, x+x=166∘⇒2x=166∘⇒x=166∘2=83∘ So, the measure of each angle is 83∘.

Question 77

The sum of two vertically opposite angles is $166^{\circ}$ . Find each of the angles.

When two lines intersect, then vertically opposite angles so formed are equal. Let x be the measure of each vertically opposite angles,
Then, $x + x = 166^{\circ} \Rightarrow 2 x = 166^{\circ} \Rightarrow x = \frac{166^{\circ}}{2} = 83^{\circ}$
So, the measure of each angle is $83^{\circ}$ .