Geometry and angle theorems

Advanced Math 5 · Unit 11 · angle-theorems-triangles · Teacher edition

angle-theorems-triangles

Name ______________________________Date ______________

1.
Two angles sit side by side on a straight line. One of them is $48^\circ$ . What is the other angle, in degrees?
Answer: ______________
2.
Two straight lines cross at point $P$ . One of the four angles at $P$ is $35^\circ$ . A third line cuts the two lines at $Q$ and $R$ , making triangle $PQR$ , and the triangle's angle at $P$ is vertically opposite the $35^\circ$ angle. The triangle's angle at $Q$ is $60^\circ$ . What is the triangle's angle at $R$ , in degrees?
Answer: ______________
3.
In triangle $ABC$ , $\angle A = 50^\circ$ and $\angle B = 60^\circ$ . Side $BC$ is extended past $C$ to a point $D$ . What is $\angle ACD$ ?
1. (A)
  $110^\circ$
2. (B)
  $70^\circ$
3. (C)
  $130^\circ$
4. (D)
  $100^\circ$

Answer key — Geometry and angle theorems

1.
132angle-theorems-triangles-01
$180^\circ - 48^\circ = \mathbf{132}^\circ$ .
2.
85angle-theorems-triangles-02
$\angle P = 35^\circ$ (vertically opposite angles are equal). Then $\angle R = 180^\circ - 35^\circ - 60^\circ = \mathbf{85}^\circ$ .
3.
(A)
$110^\circ$
angle-theorems-triangles-03
$\angle ACD = \angle A + \angle B = 50^\circ + 60^\circ = \mathbf{110}^\circ$ . Check: $\angle ACB = 70^\circ$ and $180^\circ - 70^\circ = 110^\circ$ . ✓ ( $130^\circ$ is $180^\circ - 50^\circ$ , subtracting only one interior angle; $70^\circ$ is the interior angle at $C$ , not the exterior one; $100^\circ$ is an addition slip.)