Question

the diagram below, ∠abd is a straight angle.
what is the measure of the larger angle?
select one answer
a 55° b 69°
c 125° d 180°
(3a - 2)° (5a + 30)°
a b d

Explanation:

Step1: Set up the equation

Since \(\angle ABD\) is a straight angle, its measure is \(180^\circ\). So, the sum of \((3a - 2)^\circ\) and \((5a + 30)^\circ\) is \(180^\circ\). We can write the equation:

$$ (3a - 2) + (5a + 30) = 180 $$

Step2: Solve for \(a\)

Combine like terms:

$$ 3a + 5a - 2 + 30 = 180 $$

$$ 8a + 28 = 180 $$

Subtract \(28\) from both sides:

$$ 8a = 180 - 28 $$

$$ 8a = 152 $$

Divide both sides by \(8\):

$$ a = \frac{152}{8} = 19 $$

Step3: Find the measures of the angles

First angle: \((3a - 2)^\circ\). Substitute \(a = 19\):

$$ 3(19) - 2 = 57 - 2 = 55^\circ $$

Second angle: \((5a + 30)^\circ\). Substitute \(a = 19\):

$$ 5(19) + 30 = 95 + 30 = 125^\circ $$

Step4: Identify the larger angle

Compare \(55^\circ\) and \(125^\circ\). The larger angle is \(125^\circ\).

Answer:

C \(125^\circ\)