Question

one of the exterior angle of a triangle is 105 degree. one of the interior opposite angle is 70 degree.Then other two angles are​

Answer 1

The other two angles are 35° and 75°

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Answer 2

Two Angles = 75° & 35°

Step-by-step explanation:

Given:

• Measure of exterior angle of a triangle is 105°.
• Measure of one interior opposite angle is 70°.

To Find:

• What is the measure of other two angles of triangle ?

Solution: Let the measure of another opposite interior be x°.

As we know that the sum of two interior opposite angles is equal to the measure of exterior angle.

A/q

• One angle is 70° and another is x°.

$\implies{\rm }$ 70° + x° = 105°

$\implies{\rm }$ x° = 105° – 70°

$\implies{\rm }$ x° = 35°

So we got the measures of two angles of triangle. Let the measure of third angle be y°.

Using angle sum of property :- This states that the sum of all three angles of a triangle is always equal to 180°.

$\implies{\rm }$ x° + y° + 70° = 180°

$\implies{\rm }$ 35° + y° + 70° = 180

$\implies{\rm }$ y° = 180° – (70° + 35°)

$\implies{\rm }$ y° = 180° – 105°

$\implies{\rm }$ y° = 75°

Hence, the measure of other two angles of triangle is of 75° and 35°.