Question

in the figure, ( mangle1=(x + 13)^circ ) and ( mangle2=(6x)^circ ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
( mangle1=square^circ )
( mangle2=square^circ )

Explanation:

Step1: Identify angle sum relationship

The two angles form a right angle ($90^\circ$), so their measures add to $90^\circ$.
Expression: $(x+13) + 6x = 90$

Step2: Simplify the equation

Combine like terms on the left side.
Expression: $7x + 13 = 90$

Step3: Isolate the variable term

Subtract 13 from both sides.
Expression: $7x = 90 - 13$
$7x = 77$

Step4: Solve for x

Divide both sides by 7.
Expression: $x = \frac{77}{7} = 11$

Step5: Calculate $m\angle1$

Substitute $x=11$ into $(x+13)$.
Expression: $m\angle1 = 11 + 13 = 24$

Step6: Calculate $m\angle2$

Substitute $x=11$ into $6x$.
Expression: $m\angle2 = 6 \times 11 = 66$

Answer:

(a) Equation: $(x+13) + 6x = 90$
(b)
$m\angle1 = 24^\circ$
$m\angle2 = 66^\circ$