Question

in the figure below, ( mangle 1=(x + 76)^circ ) and ( mangle 2 = 3x^circ ). find the angle measures. ( mangle 1=square^circ ) ( mangle 2=square^circ )

Explanation:

Step1: Identify supplementary angles

$\angle 1$ and $\angle 2$ form a straight line, so they are supplementary: $m\angle 1 + m\angle 2 = 180^\circ$

Step2: Substitute given expressions

$(x + 76) + 3x = 180$

Step3: Simplify and solve for $x$

Combine like terms: $4x + 76 = 180$
Subtract 76: $4x = 180 - 76 = 104$
Solve for $x$: $x = \frac{104}{4} = 26$

Step4: Calculate $m\angle 1$

Substitute $x=26$: $m\angle 1 = 26 + 76 = 102^\circ$

Step5: Calculate $m\angle 2$

Substitute $x=26$: $m\angle 2 = 3\times26 = 78^\circ$

Answer:

$m\angle 1 = 102^\circ$
$m\angle 2 = 78^\circ$