In an isosceles obtuse angled triangle the measurement of an acute
angle is half of measurement of the obtuse angle ,then find the
measurement of the obtuse angle.
Answers
Answer:
an isosceles triangle, there are two angles that are the same and one that is different. We know there is one angle that is more than
90
o
because that is the definition of an obtuse angle. We also know that the sum of all the angles of a triangle equal
180
o
. Let's put all this together and find the measures of the angles.
I'm going to call
x
the obtuse angle and
y
the acute angles.
x
+
2
y
=
180
x
=
2.5
y
Let's substitute the second equation into the first:
2.5
y
+
2
y
=
180
4.5
y
=
180
y
=
40
Which means that
x
is:
x
=
2.5
y
x
=
2.5
(
40
)
=
100
Answer link
Veddesh
ϕ
Dec 17, 2016
40
∘
,
40
∘
and
100
∘
Explanation:
In an Isoceles triangle, the two base angles are equal. Let the base angles be
x
. Then, the obtuse angle would be
2
1
2
⋅
x
enter image source here
We need to find the value of
x
Since the sum of the angles in a triangle is
180
∘
,
→
x
+
x
+
2
1
2
⋅
x
=
180
∘
→
2
x
+
2
1
2
⋅
x
=
180
∘
→
2
x
+
5
2
⋅
x
=
180
∘
→
2
x
+
5
x
2
=
180
∘
→
9
x
2
=
180
∘
→
9
x
=
360
∘
⇒
x
=
40
∘
Now we know that the base angles are
40
∘
So, the other angle is
2
1
2
⋅
40
=
100