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Find the measure of each angle indicated.
7)

Find the measure of each angle indicated. $\newline$ $7$ )

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Find missing angles in triangles

Full solution

Q. Find the measure of each angle indicated.

\newline

7

)

Add Angles in Triangle: First, let's add up all the angles in a triangle which should equal $180^\circ$ . We know one angle is $110^\circ$ , so let's call the other two angles $2x$ and $5x$ . The equation will be $110^\circ + 2x + 5x = 180^\circ$ .
Combine Like Terms: Now, let's combine like terms $2x$ and $5x$ to simplify the equation. So we get $110° + 7x = 180°$ .
Solve for x: Next, we subtract $110°$ from both sides to solve for $7x$ . That gives us $7x = 180° - 110°$ , which simplifies to $7x = 70°$ .
Find Value of x: Now, we divide both sides by $7$ to find the value of $x$ . So $x = 70° / 7$ , which means $x = 10°$ .
Calculate Unknown Angles: Finally, we can find the measures of the two unknown angles by multiplying $x$ by their respective ratios. The second angle is $2x$ , so $2 \times 10^\circ = 20^\circ$ . The third angle is $5x$ , so $5 \times 10^\circ = 50^\circ$ .

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