Question

An exterior angle of a triangle is 105 and its two interior opposite angles are equal. Each of these equal angles is:

Answer 1

$\huge\orange{QuEStiON}$

An exterior angle of a triangle is 105 and its two interior opposite angles are equal. Each of these equal angles is:

$\huge\sf \blue{Answer★}$

EXTERIOR ANGLE OF THE TRIANGLE= 105 DEGREES

AND BOTH the Interior angles are equal..

let both the equal angles be x degree each

then ,

=> 105° = x°+x°   ∵(exterior angle of a triangle is equal to the sum of interior opposite angles..)

∴ 105° = 2x°

105/2 = x°

therefore,

x° = 52.5°

Answer 2

Given, the exterior angle of a triangle is

$105 \: degrees$

Two of its interior opposite angles are equal.

We know that the exterior angle is equal to the sum of its opposite interior angles.

Let the interior angle be

$x \: degrees$

Both the interior angles are equal. Hence, both of them are

$x \: degrees$

Now,

$exterior \: angle = sum \: of \: opposite \: interior \: angles \\ 105 = x + x \\ 105 = 2x \\ x = 105 \div 2 \\ x = 52.5$

Therefore, each of the interior angles is equal to

$52.5 \: degrees$

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