Question

Suppose that ABCD is isosceles with base BC.

Answer 1

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

$4x + 19 = 2x + 33$

$4x + 19 - 2x = 33$

$4x - 2x = 33 - 19$

$2x = 14$

$x = 7$

Calculating the angles:

$∠b = 4x + 19 \\ = 4 \times 7 + 19 \\ = 47$

$∠c = 2x + 33 \\ = 2 \times 7 + 33 \\ = 47$

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

$∠b + ∠c + ∠d = 180 \\ 47 + 47 + x = 180 \\ 94 + x = 180 \\ x =180 - 94 \\ x = 86$

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