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

98°

Explanation:

I got it on Khan Academy.

In case you need some clarification:

∠ABC +∠CBD = 180°

Therefore:

2x + 50 + 6x + 2 = 180

8x + 52 = 180

8x = 128

x = 16

Input x into the formula for ∠CBD:

6(16) + 2 = 96 + 2 = 98°

Hence, the answer is 98°.

I hope this helps!

-BALL

Answer 2

m∠CBD = 98°.

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°.