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2 years ago

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

Mathematics

1 answer:

aleksandr82 [10.1K]2 years ago

5 0

Answer:

$B = 108$

$C = 36$

$D = 36$

Step-by-step explanation:

Given

$B =13x - 35$

$C = 5x - 19$

$D=2x+14$

$BC = BD$

Required

Determine the measure of each angle

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

$B + C + D = 180$

Since $BC = BD$ , then $C = D$

$B + C + D = 180$ can then be rewritten as:

$B + C + C = 180$

$B + 2C = 180$

Substitute values for B and C

$13x - 35 + 2(5x - 19) = 180$

Open Bracket

$13x - 35 + 10x - 38 = 180$

Collect Like Terms

$13x + 10x = 180 + 38 + 35$

$23x= 253$

Divide both sides by 23

$x = 11$

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

$B =13x - 35$

$B = 13 * 11 - 35$

$B = 108$

$C = 5x - 19$

$C = 5 * 11 - 19$

$C = 36$

$D=2x+14$

$D = 2 * 11 + 14$

$D = 36$

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