Question

1. in $\triangle abc$, the measures of the angles $a$, $b$, and $c$, respectively, are in the ratio $2:4:9$. what are the measures of the angles? $m\angle a = \underline{\quad\quad}^\circ$ $m\angle b = \underline{\quad\quad}^\circ$ $m\angle c = \underline{\quad\quad}^\circ$ module test \\(\cdot\\) triangles and the pythagorean theorem copyright \\(\odot\\)mcgraw-hill education. permission is granted to reproduce for classroom use.

Explanation:

Step1: Find the sum of ratio parts

The ratio of angles \( A:B:C = 2:4:9 \). Sum the ratio parts: \( 2 + 4 + 9 = 15 \).

Step2: Find the measure per part

The sum of angles in a triangle is \( 180^\circ \). So each part is \( \frac{180^\circ}{15} = 12^\circ \).

Step3: Calculate \( m\angle A \)

\( m\angle A = 2\times12^\circ = 24^\circ \).

Step4: Calculate \( m\angle B \)

\( m\angle B = 4\times12^\circ = 48^\circ \).

Step5: Calculate \( m\angle C \)

\( m\angle C = 9\times12^\circ = 108^\circ \).

Answer:

\( m\angle A = 24^\circ \), \( m\angle B = 48^\circ \), \( m\angle C = 108^\circ \)