👤
Answered

Suppose that ABCD is isosceles with base BC.
Suppose also that m 2 B = (4x+19)° and mZC= (2x +33)
Find the degree measure of each angle in the triangle.
(4x + 19)

Suppose That ABCD Is Isosceles With Base BC Suppose Also That M 2 B 4x19 And MZC 2x 33 Find The Degree Measure Of Each Angle In The Triangle 4x 19 class=

Answer :

It is an isosceles triangle which means that side BD=BC, The angles will be also equal i.e. Angle B= Angle C

Now,

  • Angle B = 4x+19
  • Angle C = 2x+33

[tex]4x + 19 = 2x + 33[/tex]

[tex]4x + 19 - 2x = 33[/tex]

[tex]4x - 2x = 33 - 19[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

Calculating the angles:

[tex]∠b = 4x + 19 \\ = 4 \times 7 + 19 \\ = 47[/tex]

[tex]∠c = 2x + 33 \\ = 2 \times 7 + 33 \\ = 47[/tex]

Now, We will find ∠D with the help of angle sum property of triangle

[tex]∠b + ∠c + ∠d = 180 \\ 47 + 47 + x = 180 \\ 94 + x = 180 \\ x =180 - 94 \\ x = 86[/tex]

The measure of angles are; 47°,47°,86° respectively...

Go Teaching: Other Questions