Question

An exterior angle of a triangle is 105° and the two interior opposite angles
differ by 15°. The smaller of the two interior opposite angles is of measure?

Answer 1

Given:

An exterior angle of a triangle is 105° and the two interior opposite angles  differ by 15°

To find:

The smaller of the two interior opposite angles is of measure?

Solution:

Since the two interior opposite angles differ by 15°, so, let's assume,

"x°" and "(15+x)°" as the measures of the two interior opposite angles of the triangle.

The exterior angle of a triangle = 105°

We know that → the sum of the two interior opposite angles of a triangle is equal to the exterior angle of the triangle.

Therefore, we can form an equation as:

$x\° + (15+x)\° = 105\°$

$\implies 2x\° + 15\° = 105\°$

$\implies 2x\° = 105\° - 15\°$

$\implies 2x\° = 90\°$

$\implies \bold{x\° = 45\°}$

∴ (x + 15)° = 45 + 15 = 60°

Thus, the measure of the smaller of the two interior opposite angles is → 45°.

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