Question

In ΔHIJ overline HJ is extended through point J to point K, m∠ JHI=(x+12)° m∠ HIJ=(x-3)° ,and m∠ IJK=(5x-6)° . Find m∠ IJK

Answer 1

The measure of angle IJK is 119°.

Step-by-step explanation:

To find the measure of angle IJK, we need to use the fact that the sum of angles in a triangle is 180 degrees.

First, we can use the given information to find the measures of angles JHI and HIJ.

m∠ JHI = (x+12)°, m∠ HIJ = (x-3)°

Since these three angles are in the same triangle, we can set up an equation:

(x+12) + (x-3) + (5x-6) = 180

Combining like terms, we get:

7x + 3 = 180

Subtracting 3 from both sides:

7x = 177

Dividing both sides by 7:

x = 25

Now we can substitute the value of x back into the given equation to find the measure of angle IJK:

m∠ IJK = 5x-6 = 5(25)-6 = 119°