Question

Exterior angle, theorem, and triangle sum theorem

Answer 1

• x = 4

Explanation:

It is assumed you are looking for the value of x.

According the diagram, we have:

• ∠JEF is exterior angle to triangle EFG and
• ∠F and ∠G are remote interior angles.

Property of exterior angle - it is same as the sum of remote interior angles.

Set equation:

• m∠F + m∠G = m∠JEF
• 16x + 4 + 14x + 6 = 130
• 30x + 10 = 130
• 30x = 120
• x = 4

It is easy to calculate the unknown angle measures if needed:

• m∠F = 16*4 + 4 = 68
• m∠G = 14*4 + 6 = 62