Question

In isosceles triangle ABC, ∠A is the vertex angle. If m∠B = (7x - 17) degrees and ∠C = (3x + 35)degrees; find the measure of ∠A​

Answer 1

Answer:

angle A = 32

Step-by-step explanation:

angle B =angle C ( isosceles property)

therefore,

7x-17=3x+35

7x-3x=35-17

4x=52

x=13

angle B =7x-17

=7×13-17

=74 degree

since angle B = angle C

angle C = 74 degree

angle A + angle B+ angle C = 180 degree( sum of all angles in a triangle is 180 degree)

angle A+ angle B +angle C= 180

angle A + 74+74 = 180

angle A = 180-74-74

angle A= 32

Answer 2

Step-by-step explanation:

Given:-

In isosceles triangle ABC, ∠A is the vertex angle. If m∠B = (7x - 17) degrees and ∠C = (3x + 35)degrees

To find:-

find the measure of ∠A

Solution:-

Given that

∆ABC is an Isosceles triangle

∠A is the vertex angle

AB=AC

we have

∠B = (7x - 17)°

∠C = (3x + 35)°

Since AB = AC

we know that

The angles opposite to equal sides are equal

=>∠B = ∠ C

=>7x -17 = 3x +35

=>7x -3x = 35+17

=>4x = 52

=>x = 52/4

=>x = 13

Now

∠B = 7x -17

=>7(13)-17

=>91-17

=>74

∠B = 74°

and

∠C = 3x +35

=>3(13)+35

=>39+35

=>74°

We know that

The sum of all angles in a triangle is 180°

=>∠A + ∠B + ∠C = 180°

=>∠A + 74°+74° = 180°

=>∠A + 148° = 180°

=>∠A = 180°-148°

=>∠A = 32°

Answer:-

The measurement of the angle A is ∠A = 32°

Used formulae:-

• In an Isosceles triangle The angles opposite to equal sides are equal.
• The sum of all angles in a triangle is 180°