Question

angles and triangles - unit test a

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question 12

1. find the measure of the largest angle in the diagram below. *

(2x)°
(3x + 10)°

Explanation:

Step1: Identify complementary angles

The two angles \(2x^\circ\) and \(3x + 10^\circ\) are adjacent and form a linear pair, so their sum is \(180^\circ\).
\[2x + (3x + 10) = 180\]

Step2: Solve for \(x\)

Combine like terms:
\[5x + 10 = 180\]
Subtract 10 from both sides:
\[5x = 170\]
Divide by 5:
\[x = 34\]

Step3: Calculate each angle

For \(2x^\circ\):
\[2(34) = 68^\circ\]
For \(3x + 10^\circ\):
\[3(34) + 10 = 102 + 10 = 112^\circ\]

Step4: Determine the largest angle

Compare \(68^\circ\) and \(112^\circ\); the largest is \(112^\circ\).

Answer:

\(112^\circ\)