Question

For triangle ABC, line AC ≅ line AB. Which set of measures is possible for angle CAB and angle CBA? (All angles look like acutes in the picture isosceles triangle

1. m∠CAB=45^∘,m∠CBA=90^∘
2. m∠CAB=20^∘ ,m∠CBA=60^∘
3. m∠CAB=30^∘,m∠CBA=30^∘
4. m∠CAB=25^∘,m∠CBA=35^∘
A) 1
B) 2
C) 3
D) 4

Answer 1

For triangle ABC with AC ≅ AB, the set of measures possible for angle CAB and angle CBA is m∠CAB=30° and m∠CBA=30°.

Step-by-step explanation:

For triangle ABC, if line AC is congruent to line AB, then the triangle is an isosceles triangle. In an isosceles triangle, the angles opposite the congruent sides are also congruent.

Looking at the given options:

1. m∠CAB=45°, m∠CBA=90°: This option does not satisfy the condition that angle CAB and angle CBA are congruent.
2. m∠CAB=20°, m∠CBA=60°: This option does not satisfy the condition that angle CAB and angle CBA are congruent.
3. m∠CAB=30°, m∠CBA=30°: This option satisfies the condition that angle CAB and angle CBA are congruent. Therefore, this set of measures is possible.
4. m∠CAB=25°, m∠CBA=35°: This option does not satisfy the condition that angle CAB and angle CBA are congruent.

Therefore, the correct answer is option C) 3.