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.
Share
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.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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
have a good day/night :)
Verified answer
The measure of one of the exterior angle is 150°.
One of the interior opposite angle is 75º.
⠀⠀⠀⠀⠀⠀⠀
We have to find, other interior opposite angle and the type of triangle.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
☯ Let the other interior opposite angle be x.
⠀⠀⠀⠀⠀⠀⠀
We know that,
⠀⠀⠀⠀⠀⠀⠀
Exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle.
⠀⠀⠀⠀⠀⠀⠀
Therefore,
[tex]:\implies\sf x + 75^\circ = 150^\circ[/tex]
⠀⠀⠀⠀⠀⠀⠀
[tex]:\implies\sf x = 150^\circ - 75^\circ[/tex]
⠀⠀⠀⠀⠀⠀⠀
[tex]:\implies{\underline{\boxed{\sf{\pink{x = 75^\circ}}}}}\;\bigstar[/tex]
⠀⠀⠀⠀⠀⠀⠀
☯ Let the third angle of the triangle be y.
⠀⠀⠀⠀⠀⠀⠀
Therefore,
[tex]:\implies\sf 75^\circ + 75^\circ + y = 180^\circ\;\;\;\;\;\;\bigg\lgroup\bf Angle\;sum\; property\;a\;\triangle \bigg\rgroup[/tex]
⠀⠀⠀⠀⠀⠀⠀
[tex]:\implies\sf 150^\circ + y = 180^\circ[/tex]
⠀⠀⠀⠀⠀⠀⠀
[tex]:\implies\sf y = 180^\circ - 150^\circ[/tex]
⠀⠀⠀⠀⠀⠀⠀
[tex]:\implies{\underline{\boxed{\sf{\purple{y = 30^\circ}}}}}\;\bigstar[/tex]
⠀⠀⠀⠀⠀⠀⠀
Since, we can see that, two angles of ∆ are equal.⠀⠀⠀
Therefore, the opposite angles are also equal.
So, The given triangle is Isosceles.
⠀⠀⠀⠀⠀⠀⠀
[tex]\therefore[/tex] The given triangle is Isosceles. And the another interior opposite angle is 75°.