Question

Two of the angles of a triangle are of measures 30 degree and 35 degree each. The triangle is
#1 an acute angled triangle.
#2 an obtuse angled triangle.
#3 a right angled triangle.
#4 (cannot be determined because measures of all the three angles are not known)

Answer 1

The third angle = 180 - 30 - 35 = 115 degrees

so its obtuse

Answer 2

The triangle will be an obtuse angled triangle

Obtuse angled triangle

A triangle whose any one of the angles is more than 90 degrees, then it is called obtuse-angled triangle.

How to solve this problem?

The steps are as follow:

• In given triangle two angle are given which are 30 degrees and 35 degree.
• To find the triangle is either acute or obtuse we have find the third unknown angle.
• If this angle will be less than 90 degree it will be acute triangle or if it will greater than 90 degree than it will be obtuse angle triangle.
• To find whether the angle is less than or greater than 90 degree it would we using following formula:

let, x = unknown angle

x + 30 + 35 = 180 because the sum of internal angle of any triangle is equal to 180 degree

x + 45 = 180

x = 180 - 45

x = 115 degree

Since the unknown angle is greater than 90 degree the triangle will be  an obtuse angled triangle.

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