Question

5. In an isosceles triangle, the vertical angle is 6° more
than a base angle. Find the measures of all the angles
of the triangle​

Answer 1

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✤ Required Answer:

✒ GiveN:

• Here is an Isoceles triangle
• The vertical angle is 6° more than the base angles$.$

✒ To FinD:

• Measure of all angles of the triangle...?

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✤ How to solve?

First let's note down some important points in order to solve this question:-

• Angles opposite to equal sides are equal. Like in case of isoceles or in equilateral triangle.
• Angles of any triangle add upto 180°

☃️ So, By keeping these points in mind, Let's solve this question....

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✤ Solution:

Let each of the base angles be x

Then,

➝ Vertical angle will be x + 6

We know,

➝ Angles of the triangle add upto 180°

So,

➝ Vertical angle + 2 × Base angles = 180°

➝ x + 6 + 2x = 180°

➝ 3x = 180° - 6°

➝ 3x = 174°

➝ x = 58°

So, Our required angles are:

• Vertical angle = x + 6 = 64°
• Base angle = x = 58°
• Another base angle = x = 58°

✏️ Hence, solved !!

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