Question

One of the exterior angle of a angle.ABC measures 150°. If one
of the interior opposite angle is 75º. Find the other interior
opposite angle. What type of triangle is this?
.
please!!! can any one tell me the answer with a help of diagram.​

Answer 1

Answer:

The three angles are 75° , 75° and 30°. It is an acute angled triangle

Step-by-step explanation:

Please see the attachment for the following.

Hope this helps

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Answer 2

The measure of one of the exterior angle is 150°.

One of the interior opposite angle is 75º.

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We have to find, other interior opposite angle and the type of triangle.

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☯ Let the other interior opposite angle be x.

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We know that,

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Exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle.

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Therefore,

$:\implies\sf x + 75^\circ = 150^\circ$

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$:\implies\sf x = 150^\circ - 75^\circ$

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$:\implies{\underline{\boxed{\sf{\pink{x = 75^\circ}}}}}\;\bigstar$

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☯ Let the third angle of the triangle be y.

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Therefore,

$:\implies\sf 75^\circ + 75^\circ + y = 180^\circ\;\;\;\;\;\;\bigg\lgroup\bf Angle\;sum\; property\;a\;\triangle \bigg\rgroup$

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$:\implies\sf 150^\circ + y = 180^\circ$

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$:\implies\sf y = 180^\circ - 150^\circ$

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$:\implies{\underline{\boxed{\sf{\purple{y = 30^\circ}}}}}\;\bigstar$

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Since, we can see that, two angles of ∆ are equal.⠀⠀⠀

Therefore, the opposite angles are also equal.

So, The given triangle is Isosceles.

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$\therefore$ The given triangle is Isosceles. And the another interior opposite angle is 75°.