Question

m∠ABDm, angle, A, B, D is a straight angle.

\qquad m \angle ABC = 2x + 50^\circm∠ABC=2x+50

∘

m, angle, A, B, C, equals, 2, x, plus, 50, degrees

\qquad m \angle CBD = 6x + 2^\circm∠CBD=6x+2

∘

m, angle, C, B, D, equals, 6, x, plus, 2, degrees

Find m\angle CBDm∠CBDm, angle, C, B, D:

Answer 1

Answer:

m∠CBD = 98°.

Step-by-step explanation:

Given information: ∠ABD is a straight angle, m∠ABC=2x+50° and m∠CBD=6x+2°.

∠ABD is a straight angle, it means m∠ABD is 180°.

$\angle ABD=180^{\circ}$

From the below graph we can conclude that

$\angle ABC+ \angle CBD=\angle ABD$

$(2x+50)+(6x+2)=180$

Combine like terms.

$(2x+6x)+(50+2)=180$

$8x+52=180$

$8x=180-52$

$8x=128$

Divide both sides by 8.

$x=16$

The value of x is 16.

We need to find the m∠CBD.

$\angle CBD=6x+2$

$\angle CBD=98$

Therefore, the value of m∠CBD is 98°.