Question

I need help please! If m∠ABD=76°​, what are m∠ABC and m∠​DBC? If m∠JKH=77° then m∠NDF=​__

Answer 1

Answer:

m<ABC = 41°

m<DBC = 35°

m<NDF = 77°

Step-by-step explanation:

Problem 1:

Given, m<ABD = 76°, m<ABC = (7x - 1), m<DBC = (5x + 5)

m<ABC + DBC = m<ABD (angle addition postulate)

$(7x - 1) + (5x + 5) = 76$ (substitution)

Solve for x

$7x - 1 + 5x + 5 = 76$

Collect like terms

$7x + 5x - 1 + 5 = 76$

$12x + 4 = 76$

Subtract 4 from each side

$12x + 4 - 4 = 76 - 4$

$12x = 72$

Divide each side by 12

$x = 6$

Find m<ABC

m<ABC = (7x - 1)

Plug in the value of x

m<ABC = 7(6) - 1 = 42 - 1 = 41°

Find m<DBC

m<DBC = (5x + 5)

Plug in the value of x

m<DBC = 5(6) + 5 = 30 + 5 = 35°

Problem 2:

<JKH and <NDF are corresponding angles. Corresponding angles are congruent.

Given that m<JKH = 77°, m<NDF = 77° (corresponding angles are equal).