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Find the missing angles

Find the missing angles

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Find missing angles in triangles

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Q. Find the missing angles

Set Up Equation: Since the sum of angles in a triangle is always $180^\circ$ , we can set up an equation with the given angle and the ratio of the other two angles. $\newline$ Let's call the smaller angle $2x$ and the larger angle $5x$ . $\newline$ So, we have $110^\circ + 2x + 5x = 180^\circ$ .
Combine Like Terms: Now, let's combine like terms $(2x + 5x)$ to simplify the equation. $110° + 7x = 180°$ .
Subtract and Solve: Next, we'll subtract $110°$ from both sides to solve for $7x$ . $\newline$ $7x = 180° - 110°$ . $\newline$ $7x = 70°$ .
Find Value of x: Now, we divide both sides by $7$ to find the value of x. $\newline$ $x = \frac{70°}{7}$ . $\newline$ $x = 10°$ .
Find Missing Angles: We can now find the measures of the two missing angles by multiplying $x$ by $2$ and by $5$ . The smaller angle is $2x$ , which is $2 \times 10° = 20°$ . The larger angle is $5x$ , which is $5 \times 10° = 50°$ .

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