Question

one of the exterior angles of a triangle is 90 Degrees and its interior opposite angles are equal to each other. find the measure of the two equal angles of the triangle.

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Answer 1

Given:

• An exterior angle of triangle is 90°

Find:

• Measure of interior angles

Solution:

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Let, the interior angle be x

So, other will also be (x) because it is given both are equals

we, know that

$\boxed{ \sf Sum \: of \: Opposite \: Interior \: angle = Exterior \: angle }$

where,

• Interior Angles are x or x
• Exterior angle = 90°

So,

$\dashrightarrow\sf Sum \: of \: Opposite \: Interior \: angle = {90}^{ \circ} \\ \\ \\ \dashrightarrow\sf x + x= {90}^{ \circ} \\ \\ \\ \dashrightarrow\sf 2x= {90}^{ \circ} \\ \\ \\ \dashrightarrow\sf x= \dfrac{{90}^{ \circ}}{2} \\ \\ \\ \dashrightarrow\sf x= {45}^{ \circ}$

$\therefore\sf x= {45}^{\circ}$

____________________________

Hence, Both angles are of 45°

Answer 2

Answer:

45°

Step-by-step explanation:

Let, the interior angle be x

So, other will also be (x) because it is given both are equals

we, know that

Sum of Opposite Interiorangle=Exterior angle

where,

Interior Angles are x or x

Exterior angle = 90°

So,

⇢x+x=90°

⇢2x=90°

∘

⇢x= 2/90

⇢x=45°