Question

3 G 1 Н 5 2 7 6 3 4 к Quadrilateral GHJK is a rectangle. Find the measure of angle 2, given that the measure of angle 4 is 54°. * (1 Point) 54° 360 126 134° Ps 15% search DI

Answer 1

Since quadrilateral GHJK is a rectangle, then triangle GKJ will be a right triangle. And therefore, the angle GKJ will be a right angle, that is, 90°. Then, you have

Now, the triangle Sum Theorem says that the sum of the three interior angles in a triangle is always 180°, then you have

`\begin{gathered} m\angle2+m\angle GKJ+m\angle4=180\text{\degree} \\ m\angle2+90\text{\degree}+54\text{\degree}=180\text{\degree} \\ m\angle2+144\text{\degree}=180\text{\degree} \\ \text{ Subtract 144\degree{}from both sides of the equation} \\ m\angle2+144\text{\degree}-144\text{\degree}=180\text{\degree}-144\text{\degree} \\ m\angle2=36\text{\degree} \end{gathered}`

Therefore, the measure of angle 2 is 36°, given that the measure of angle 4 is 54°. And the correct answer is B. 36°.