Question

find missing angles quick check
in a geometric diagram, ∠a and ∠b are complementary, and they form a straight line with ∠c. if ( mangle a = x^circ ), ( mangle b = (2x)^circ ), and ( mangle c = 90^circ ), what is the measure of ( angle b )? (1 point)
options: ( 180^circ ), ( 30^circ ), ( 90^circ ), ( 60^circ )

Explanation:

Step1: Use straight line angle sum

$\angle A + \angle B + \angle C = 180^\circ$

Step2: Substitute given angle values

$x + 2x + 90 = 180$

Step3: Simplify and solve for $x$

$3x = 180 - 90$
$3x = 90$
$x = 30$

Step4: Calculate $m\angle B$

$m\angle B = 2x = 2\times30 = 60$

Answer:

$\boldsymbol{60^\circ}$ (Option: $\boldsymbol{\bigcirc 60^\circ}$)