Two adjacent angles are inside a 90° angle. One angle has a measure of (x+4)° and the other angle has a measure of (3x+2)° . What is x ?

Since the two adjacent angles are inside a 90° angle, their measures should add up to 90°.

So, (x+4) + (3x+2) = 90

Combining like terms, we get 4x + 6 = 90.

Subtracting 6 from both sides gives 4x = 84.

Finally, dividing both sides by 4 gives x = 21.

Therefore, x is equal to 21.

Two adjacent angles form a resulting angle with measure 160° . m∠1=3x° and m∠2=(2x+10)° . Solve for x . What are the two unknown angles’ measurements?

Since the resulting angle is formed by two adjacent angles, their measures should add up to 160°.

So, 3x + (2x+10) = 160

Combining like terms, we get 5x + 10 = 160.

Subtracting 10 from both sides gives 5x = 150.

Finally, dividing both sides by 5 gives x = 30.

To find the measures of the angles, we substitute the value of x back into the expressions for their measures:

m∠1 = 3x = 3(30) = 90°
m∠2 = 2x+10 = 2(30) + 10 = 60 + 10 = 70°

Therefore, the two unknown angles' measurements are 90° and 70°.

An illustration shows three rays extending from a common origin. The angle measures between them are labeled.

What are the two unknown angle measures that form the 90° angle?

In the illustration, two rays are shown extending from a common origin, forming an angle labeled as 90°. Since we are looking for the unknown angle measures that form this 90° angle, these unknown angles will be adjacent to the 90° angle.

Adjacent angles to a 90° angle are always complementary, meaning their measures add up to 90°.

Therefore, the two unknown angle measures that form the 90° angle would each be equal to (90° - 90°) / 2 = 0°.

Hence, the two unknown angle measures that form the 90° angle are both 0°.