Question

M∠JIH is 107 degrees and m∠JDI is 31 degrees. What is m∠AJF?

Answer 1

m∠AJF is 76°

Explanation:

Given:

`\sf m\angle JIH = 107^\circ`

`\sf m\angle JDI = 31^\circ`

To find:

`\sf m\angle AJF = x`

Solution:

`\sf m\angle DJI =m\angle AJB = x`

Since vertically opposite angles are equal.

Again,

`\sf m\angle DJI + m\angle JDI = m\angle JIH`

Since, exterior angle of a triangle is equal to the sum of two opposite interior angles.

Substitute the value:

`\sf x + 31^\circ =107^\circ`

Subtract 31° from both sides:

`\sf x + 31^\circ -31^\circ =107^\circ- 31^\circ`

Solve it:

`\sf x = 76^\circ`

Therefore m∠AJF is 76°.