We read your photo as:

Is the angle formed by MH and MJ acute, obtuse, or straight?

Mathematics

ScanSolve AI Answer

Step-by-step solution

6 steps

Here are the answers based on the provided image:

  1. Classify the angle for question 14.

    The angle shown next to "14." is visually larger than 90∘90^\circ but less than 180∘180^\circ. 14. The angle shown is an obtuse angle.

  2. Calculate and classify ∠HMJ\angle H M J.

    From the diagram, the measure of ∠HMJ\angle H M J is given as 60∘60^\circ.
    Since 60∘<90∘60^\circ < 90^\circ, it is an acute angle.
    ∠HMJ=60∘\angle H M J = \boxed{\text{}60^\circ\text{}} (Acute angle)

  3. Calculate and classify ∠JMK\angle J M K.

    From the diagram, the measure of ∠JMK\angle J M K is given as 30∘30^\circ.
    Since 30∘<90∘30^\circ < 90^\circ, it is an acute angle.
    ∠JMK=30∘\angle J M K = \boxed{\text{}30^\circ\text{}} (Acute angle)

  4. Calculate and classify ∠HMK\angle H M K.

    ∠HMK\angle H M K is the sum of ∠HMJ\angle H M J and ∠JMK\angle J M K.

    ∠HMK=∠HMJ+∠JMK\angle H M K = \angle H M J + \angle J M K ∠HMK=60∘+30∘\angle H M K = 60^\circ + 30^\circ ∠HMK=90∘\angle H M K = 90^\circ

    Since ∠HMK=90∘\angle H M K = 90^\circ, it is a right angle.
    ∠HMK=90∘\angle H M K = \boxed{\text{}90^\circ\text{}} (Right angle)

  5. Calculate and classify ∠LMJ\angle L M J.

    Let L be the point on the leftmost ray. ∠LMJ\angle L M J is the sum of ∠LMH\angle L M H and ∠HMJ\angle H M J.

    ∠LMJ=∠LMH+∠HMJ\angle L M J = \angle L M H + \angle H M J ∠LMJ=50∘+60∘\angle L M J = 50^\circ + 60^\circ ∠LMJ=110∘\angle L M J = 110^\circ

    Since 90∘<110∘<180∘90^\circ < 110^\circ < 180^\circ, it is an obtuse angle.
    ∠LMJ=110∘\angle L M J = \boxed{\text{}110^\circ\text{}} (Obtuse angle)

  6. Calculate and classify ∠LMN\angle L M N.

    Let L be the point on the leftmost ray and N be the point on the rightmost ray. ∠LMN\angle L M N is the sum of all angles along the straight line.

    ∠LMN=∠LMH+∠HMJ+∠JMK+∠KMN\angle L M N = \angle L M H + \angle H M J + \angle J M K + \angle K M N ∠LMN=50∘+60∘+30∘+40∘\angle L M N = 50^\circ + 60^\circ + 30^\circ + 40^\circ ∠LMN=180∘\angle L M N = 180^\circ

    Since ∠LMN=180∘\angle L M N = 180^\circ, it is a straight angle.
    ∠LMN=180∘\angle L M N = \boxed{\text{}180^\circ\text{}} (Straight angle)

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp