Question

question 17
in the figure, ( mangle 1=(x + 51)^circ ) and ( mangle 2=(2x)^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.
( mangle 1=square^circ )
( mangle 2=square^circ )

Explanation:

Step1: Recognize right angle sum

The two angles form a right angle ($90^\circ$), so their measures add to $90^\circ$.
$m\angle 1 + m\angle 2 = 90^\circ$
Substitute given expressions:
$(x+51) + 2x = 90$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$3x + 51 = 90$
$3x = 90 - 51$
$3x = 39$
$x = \frac{39}{3} = 13$

Step3: Calculate $m\angle 1$

Substitute $x=13$ into $m\angle 1=(x+51)^\circ$.
$m\angle 1 = 13 + 51 = 64$

Step4: Calculate $m\angle 2$

Substitute $x=13$ into $m\angle 2=(2x)^\circ$.
$m\angle 2 = 2\times13 = 26$

Answer:

(a) Equation: $(x+51)+2x=90$
(b) $m\angle 1 = 64^\circ$
$m\angle 2 = 26^\circ$