In Triangle BCD, BC=BD, and angle B =13x-35, angle C = 5x-19, angle D=2x+14. Find the measure of each angle

The measure of m<B, m<C and m<D are 108, 36 and 46 respectively

From the triangle BCD, if BC=BD, then

m<C = m<D (Base angles are equal)

Given the following paramters:

Hence;

5x - 19 =2x + 14

5x- 2x = 14 + 19

3x = 33

x = 11

m<B = 13x - 35

m<B = 13(11) - 35

m<B = 108 degres

m<C = 5x - 19

m<C = 55- 19

m<C = 36

m<D = 180 - 144

m<D = 36 degreees

Hence the measure of m<B, m<C and m<D are 108, 36 and 46 respectively

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Step-by-step explanation:

Given

Required

Determine the measure of each angle

The angles in a triangle sum up t 180. i.e.

Since , then

can then be rewritten as:

Substitute values for B and C

Open Bracket

Collect Like Terms

Divide both sides by 23

To get the measure of each angle, substitute 11 for x in the expressions of B, C and D