Question

An exterior angle of a triangle is 105 degree and its two interior opposite angles are equal. Find all the interior angles.​

Answer 1

Answer and Step-by-step explanation:

Question

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

• A.37.5∘

• B.52.5∘

• C.72.5∘

• D.75∘

Solution

The correct option is B.52.5∘

From the properties of triangles:

Exterior angle = Sum of interior opposite angles

Now let us take each interior opposite angle as x ( as both interior opposite angles are equal)

⇒ x + x = 105∘

⇒ 2x = 105∘

⇒ x = 52.5∘

So the value of each of the opposite interior angle = 52.5∘

Answer 2

According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles. In this case, the exterior angle is 105 degrees, and its two interior opposite angles are A and B.

So we have the equation:

A + B = 105 (equation 1)

Given that the two interior opposite angles are equal, we can also express this as:

A = B (equation 2)

Substituting equation 2 into equation 1, we get:

2A = 105

Dividing both sides by 2, we find:

A = 52.5

Since A = B, we also have B = 52.5.

To find the third angle C, we know that the sum of the interior angles of a triangle is always 180 degrees. So:

A + B + C = 180

Substituting the values we found for A and B, we get:

52.5 + 52.5 + C = 180

Simplifying the equation, we find:

105 + C = 180

Subtracting 105 from both sides, we have:

C = 75

Therefore, the three interior angles of the triangle are:

A = 52.5 degrees

B = 52.5 degrees

C = 75 degrees