Question

1. find m∠yrs.
2. find m∠s.

a) 30° b) 146°
c) 145° d) 150°
a) 73° b) 54°
c) 57° d) 72°

Explanation:

Step1: Use exterior - angle property of a triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the first triangle, $\angle YRS$ is an exterior angle, so $29x=115+(7x - 5)$.

Step2: Solve the equation for $x$

First, simplify the right - hand side of the equation: $29x=115 + 7x-5=110 + 7x$. Then, subtract $7x$ from both sides: $29x-7x=110$, which gives $22x = 110$. Divide both sides by 22: $x = 5$.

Step3: Find $m\angle YRS$

Substitute $x = 5$ into the expression for $\angle YRS$ (which is $29x$). So $m\angle YRS=29\times5=145^{\circ}$.

Step4: For the second triangle, use exterior - angle property

The exterior angle of the second triangle is $127^{\circ}$, and by the exterior - angle property of a triangle, $127=(8x - 2)+(10x + 3)$.

Step5: Solve the equation for $x$

Simplify the right - hand side: $127=8x-2 + 10x+3=18x + 1$. Subtract 1 from both sides: $127-1=18x$, so $126 = 18x$. Divide both sides by 18: $x = 7$.

Step6: Find $m\angle S$

Substitute $x = 7$ into the expression for $\angle S$ (which is $10x + 3$). So $m\angle S=10\times7+3=73^{\circ}$.

Answer:

1. C. $145^{\circ}$
2. A. $73^{\circ}$