Question

one of the two equal angles of an isoscles triangle measure 55 degree
. determine the other angle
​

Answer 1

Answer :

• The others angles are 70⁰ and 55⁰

Given :

• One of the two angles of an iscoscles triangle measure is 55⁰

To find :

• The other angle

Solution :

Given that ,

• One of the two angles of an iscoscles triangle measure 55⁰

As we know that,

• Sum of all interior angles of a triangle is equal to 180⁰

Then

• Let the angles be ∠A, ∠B ,∠C
• ∠B = ∠C= 55⁰

》∠A + ∠B + ∠C = 180⁰

》 ∠A + 55⁰ + 55⁰ = 180⁰

》 ∠A + 110⁰ = 180⁰

》 ∠A = 180⁰ - 110⁰

》 ∠A = 70⁰

Hence , The others angles are 70⁰ and 55⁰

Verification:

As we know that,

• Sum of all interior angles is 180⁰

》 ∠A + ∠B + ∠C = 180⁰

》 70⁰ + 55⁰ + 55⁰ = 180⁰

》 70⁰ + 110⁰ = 180⁰

》 180⁰ = 180⁰

Hence Verified

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

Let us assume that ABC is an isosceles triangle with AB = AC.

So, that

• ∠B = ∠C = 55°

Since,

We know that,

• Sum of angles of a triangle is 180°.

So,

In triangle ABC,

• ∠A + ∠B + ∠C = 180°.

• ∠A + 55° + 55° = 180°

• ∠A + 110° = 180°

• ∠A = 180° - 110°

• ∠A = 70°

Hence,

$\boxed{ \pink{\begin{gathered}\begin{gathered}\bf \: Angles \: of \: \triangle \: are \:  - \begin{cases} &\sf{ \angle \: A \: = \: 70 \degree} \\ &\sf{\angle \:B \: = \: 55\degree}\\ &\sf{\angle \:C \: = \: 55\degree} \end{cases}\end{gathered}\end{gathered}}}$

Explore more :-

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.